arXiv:2001.11689v2 [astro-ph.CO] 4 Aug 2020 2,rsetvl.GvnteS n h i parame- sub- spectra six incorporate power four the that C with [3–5] and us provides codes astrophysics SA sequent Boltzmann the the Given epoch ters, the reionization respectively. the and characterizes oscillations, [2], that acoustic depth with optical associated scale lar e,rsetvl,t ayncadtecl atrden- matter cold 100 the and and baryonic sity; to respectively, fer, where hc ewl ee oa h tnadast (SA): ansatz standard form, the specific as to a refer with will invariant power we scale infla- primordial which by nearly the Inspired is that assumes spectrum data. one CMB deter- models, the to used tionary from is model Let that the procedure [1]. mine the temperature recalling parameters by the six begin microwave only us cosmic in using success the (CMB), features of impressive background polarizations major had and all anisotropies has explaining data in satellite PLANCK zto oe spectrum power ization oe n bevto.W ilinr h eso be- tension the ignore low- ΛCDM will and CMB We best-fit the tween the observation. between and tensions model out bring that lies 10]. 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[6, tential ture, oe)T eemn pcfi CMmdl n re- one Ω model, parameters: ΛCDM additional specific four a quires determine To mode.) ℓ T T Introduction.— ttesm ie h M aaehbtsm anoma- some exhibit data CMB the time, same the At C , E A md ee-aiy oaiain n esn po- lensing and polarization, (even-parity) -mode ℓ E T s C , steapiueo h clrmd and mode scalar the of amplitude the is A pia et n oe upeso nthe in suppression power and depth optical eedn o small for dependent esn mltd.Teedffrne rs eas,i LQC, p qua in large-scale loop because, the arise with differences both analysis These alleviates PLANCK LQC amplitude. the lensing that revisit show We and data. dictions CMB the and L ℓ 3 EE θ eti nmle nteCBbigotatninbtentes the between tension a out bring CMB the in anomalies Certain ∗ 8,adthe and [8], 2 eateto hsc,Ntoa nttt fTcnlg Ka Technology of Institute National Physics, of Department , P leitn h eso nteCsi irwv Background Microwave Cosmic the in Tension the Alleviating C , nttt o rvtto n h oms&Dprmn fAst of Department & Cosmos the and Gravitation for Institute h CMmdlslce ythe by selected model ΛCDM The τ R ( ℓ φφ htdtrieteosre angu- observed the determine that k = ) , ba Ashtekar, Abhay where z C A bevtos n ou instead focus and observations, ℓ BB 1 enSaeUiest,Uiest ak enyvna1680 Pennsylvania Park, University University, State Penn enSaeUiest,Uiest ak enyvna1680 Pennsylvania Park, University University, State Penn k s ⋆ B nttt o rvtto n h oms&PyisDepartme Physics & Cosmos the and Gravitation for Institute  0 = esrsteapiueof amplitude the measures md odprt)polar- (odd-parity) -mode ,E φ E, T, k k k ⋆ ihaseicpwrsprsin ecnld ihapredic a with conclude We suppression. power specific a with , .  5Mpc 05 n s − tn o tempera- for stand b 1 h , 1 2 sn lnkSaePhysics Planck-Scale using , − rjs Gupt, Brajesh Ω 1 c stepivot the is h 2 htre- that B (1) n md oaiainpwrsetu nlrescales. large on spectrum power polarization -mode s 1 ogu Jeong, Donghui bandb nertn h w-on orlto func- correlation two-point the tion integrating by obtained ag nua cls( scales angular large n LNK[3 4 esrdvle of values measured 14] [13, PLANCK and ntoaoaisi h M.Tefis stelarge-scale to the related is first anomaly The power CMB. the in anomalies two on oaiainpwrspectrum. power polarization ttebgbn,i remains it bang, big the at on l hsclqatte eanfiie nparticu- In curvature scalar finite. the remain while quantities lar, Since break physical never [23–34]). all equations down, Refs. Einstein’s corrected e.g., quantum (see, one the starting regime Planck epoch Therefore, the pre-inflationary from the 22]). in [21, cosmolog- perturbations of ical dynamics Refs. the investigate a e.g., systematically by can (see, replaced and bounce resolved big naturally is singularity bang the in signature specific higher a and leaves spectrum power primordial modified and depth ΛCDM), optical flat higher with consistent it (making unity toward eedn rmrilpwrsetu,i un rfr a prefers amplitude turn, in higher spectrum, power primordial dependent ooy h eodi h nml soitdwt the with associated anomaly amplitude cos- the SA+ΛCDM is lensing second the The from mology. expectation the than smaller nrdc oalvaeti eso ae M analysis CMB makes low- tension can with cos- this inconsistent one in curvature alleviate crisis spatial to “possible positive [20] introduce a the suggested to recently because rise was mology” gives it anomaly particular, this based In that 15–19] internal SA. [7, an the cosmology at on ΛCDM hinting the unity, in than inconsistency larger value a prefers ue hc aual ed olower to leads naturally ampli- which large-scale its tude, suppressing primor- by the for spectrum SA power (LQC). the dial modifies cosmology prediction quantum LQC the loop First, the- of well-motivated framework a within oretical anomalies both alleviating oie rmrilpwrspectrum.— power primordial Modified nti etr epeeta nrgigpsiiiyof possibility intriguing an present we Letter, this In C ( the θ fteCBtmeaueaiorpe over anisotropies temperature CMB the of ) wraoayadtetnini the in tension the and anomaly ower primordial ntk,Srtkl ni 575025 India Surathkal, rnataka, 2 xprmtrfltΛD model ΛCDM flat ix-parameter n .Sreenath V. and ooyadAstrophysics, and ronomy tmcsooy(Q)pre- (LQC) cosmology ntum A A s L τ htpse esn amplitude lensing pushes that oe pcrmi scale is spectrum power z hni salwdt vary, to allowed is it When . ial eso ht u othe to due that, show we Finally . > θ ,USA 1, ,USA 1, omlgclmeasurements. cosmological nt, S 60 finite 1 / ◦ 2 .TeWA 1,12] [11, WMAP The ). R ino larger of tion 3 ≡ ttebuc,achiev- bounce, the at fsaetm diverges space-time of B R md (odd-parity) -mode − 1 / 1 S 2 1 [ nLC h big the LQC, In / C 2 S h scale- The . ( 1 θ / )] 2 2 r much are d τ (cos LQC , A A θ ), L L 2

ns−1 ing its universal maximum value Rmax ≈ 62 in Planck LQC k PR = f(k) As , (2) units. Now, curvature—more precisely R/6—provides  k⋆  a natural scale in the dynamics of the gauge invariant where the form of the suppression factor f(k) can be seen perturbations (which in de Sitter space-time coincides in Fig.1. [f(k) ≈ 1 for k ≫ k◦.] This difference from the with 2H2). Fourier modes with physical wave num- standard ansatz can be traced back directly to the modes bers k ≡ k/a(η) ≫ (R/6)1/2 are essentially unaf- phys not being in the BD vacuum at the onset of inflation. fected by curvature while those with k . (R/6)1/2 phys Now, if the total energy in the scalar field is dominated get excited. Therefore the evolution during the pre- by the kinetic contribution at the bounce, details of the inflationary epoch of LQC is subject to a new scale: potential do not affect the preinflationary dynamics, and k = (R /6)1/2 ≈ 3.21 in Planck units. Modes LQC max the suppression factor f(k) is also the same. Analysis with kB . k at the bounce are excited during their phys LQC of Ref. [38] strongly suggests that there is a large class preinflationary evolution. Therefore they are not in the of potentials for which our proposal to choose the back- Bunch Davies (BD) vacuum at the onset of the relevant ground geometry will constrain the bounce to be kinetic slow roll phase of inflation—i.e., a couple of e-folds before energy dominated. This is illustrated by comparing the the time at which the mode with the largest observable Starobinsky inflation [39] and the quadratic potential in wavelength crosses the Hubble horizon during inflation. Fig.1. (For details, see Refs. [23, 24]). Now, one’s first reaction may be that these excitations are observationally irrelevant because they would be sim- 1.0 ply diluted away by the end of inflation. However, this is . not the case: because of stimulated emission, the number 0 8 P density of these excitations remains constant during in- LQC PSA 0.6 flation [22, 35, 36]. Therefore the primordial LQC power spectrum at the end of inflation is different from the stan- 0.4 B dard ansatz of Eq. (1) for modes with kphys < kLQC. Starobinsky Potential 0.2 The key question then is whether these long wave- Quadratic Potential length modes are in the observable range. The answer . 0 0 −5 −4 −3 −2 depends on the choice of the background metric that sat- 10 10 10 10 k −1 isfies the quantum corrected Einstein’s equations of LQC, [Mpc ] and the Heisenberg state of the cosmological perturba- tions. In standard inflation, the background metric can FIG. 1: Ratio of the primordial scalar-power spectrum for be any solution of Einstein’s equation for the given poten- LQC and SA. Power is suppressed in LQC for k . 10k◦ ≃ − − tial, and, since one cannot specify the quantum state of 3.6 × 10 3Mpc 1. Plots for the Starobinsky and quadratic perturbations at the big bang, one specifies it, so to say, potentials are essentially indistinguishable. in the middle of the evolution by asking that they be in the BD vacuum at the start of the relevant phase of the slow roll. In LQC, geometry is regular at the bounce. 6000 LQC Using this fact, key features of the quantum geometry SA

] Planck 2018 in LQC, and a “quantum generalization” of Penrose’s 2 5000 µK

Weyl curvature hypothesis [37], a specific proposal has [

π 4000 been put forward to make the required choices [30, 31]. 2 / TT Quantum corrected LQC dynamics then leads to unique ℓ 3000 predictions for the primordial power spectrum for any C

given inflationary potential; there are no parameters to + 1) 2000 ℓ (

adjust. The viewpoint is to use the proposal as a working ℓ hypothesis, analyze the consequences, and use the CMB 1000 observations to test its admissibility. 0 2 10 20 30 40 1000 2000 The proposal constrains the background metric to be ℓ such that the ΛCDM universe has undergone ≃ 141 e- folds since the bounce (irrespective of the choice of in- FIG. 2: TT power spectra. The 2018 PLANCK spectrum flationary potential) [30]. It then follows that the mode (black dots with error bars), the LQC [solid (blue) line], and with kphys = kLQC at the bounce has comoving wave the standard ansatz predictions [dashed (red) line]. − −1 number k◦ ≃ 3.6 × 10 4Mpc . The primordial power spectrum of LQC is nearly scale invariant for k ≫ k◦ but Results.—All results are based on the PLANCK-2018 power is suppressed for k . 10k◦: data [1] using the observed TT, TE, EE, and φ-φ power 3 spectra (including the ℓ < 30 modes for EE correla- Parameter SA LQC 2 tions) to which the associated likelihoods are Planck Ωbh 0.02238 ± 0.00014 0.02239 ± 0.00015 2 TTTEEE+lowl+lowE+Lensing. Ωch 0.1200 ± 0.0012 0.1200 ± 0.0012 ± ± Figure 2 shows the observed TT-power spectrum to- 100θMC 1.04091 0.00031 1.04093 0.00031 gether with the 1σ (68% confidence level) error bars, and τ 0.0542 ± 0.0074 0.0595 ± 0.0079 10 the LQC and the SA predictions for the respective best- ln(10 As) 3.044 ± 0.014 3.054 ± 0.015 fit cosmological parameters. Clearly, LQC power is sup- ns 0.9651 ± 0.0041 0.9643 ± 0.0042 S . . pressed at ℓ . 30 relative to the SA. This is also true for 1/2 42496 5 14308 05 the EE power spectrum (as already noted in Ref. [30], us- ing the then available PLANCK 2015 data). Note that TABLE I: Comparison between the standard ansatz and the difference between LQC and SA best-fitting curves LQC. The mean values of the marginalized PDF for the six cosmological parameters, and values of S1 2 calculated using shown in Fig. 2 underestimates the difference in the pre- / CTT. dicted primordial spectra, for the best-fitting cosmologi- ℓ cal parameters are different. Also, had the LQC+ΛCDM model been used for their analysis, the cosmic-variance uncertainties on large scales may have been smaller than Table I also shows the mean values of the marginalized the reported values from PLANCK 2018. probability distributions of the six cosmological param- Figure 3 compares the angular TT two-point corre- eters together with their 1σ ranges. For the first three, lation function C(θ) predicted by LQC with that pre- 2 2 namely, Ωbh ,Ωch , and 100θMC, the difference between dicted by the SA. It is clear by inspection that the LQC the SA+ΛCDM and LQC+ΛCDM values is < 0.07σ and prediction for C(θ) is closer to the observed values for for ns the difference is ∼ 0.2σ. However, the values of the all θ. In order to quantify this difference, we computed 10 optical depth τ and ln(10 As) have increased in LQC by S1/2. As the last row of Table I shows, the S1/2 from 0.72σ. As we discuss below, this significant change is a the best-fit LQC+ΛCDM model is about a third of that direct consequence of the scale-dependent initial power obtained from SA+ΛCDM, and closer to the value of spectrum (2) of LQC, which also leads to a 0.56σ de- S1/2 = 1209.2 given by the PLANCK Collaboration us- crease in the lensing amplitude AL from 1.072 ± 0.041 in ing the Commander CMB map. But since that value is SA+ΛCDM to 1.049 ± 0.040 in LQC+ΛCDM, when AL obtained after masking and additional processing, a more is also varied. Furthermore, when AL is included in the appropriate comparison would be with the value 6771.7 analysis, the ΛCDM parameters change by 0.59σ − 1.48σ of S1/2 obtained from the full sky map, i.e. using the in SA and 0.39σ − 1σ in LQC. As Fig. 4 shows, the value PLANCK CT T data for all ℓ. The difference between AL = 1 lies outside of the 68% confidence level for the LQC and this PLANCK value is also significantly lower SA+ΛCDM model (red contours). A natural way to al- than that between SA and this PLANCK value. This leviate this tension within the SA+ΛCDM is to consider a is a substantial alleviation of the tension between the- closed universe. However, then other disagreements with ory and observations that has been emphasized over the observations arise that prompted the authors of Ref. [20] years [11–14]. to raise the possibility of a “crisis in cosmology.” What is the situation with the altered values of τ and AL in 1500 LQC? We see from Fig. 4 that now the tension is natu- LQC 1250 rally alleviated because the value AL = 1 is within 68% SA confidence level (blue contours). Therefore, the primary 1000 Planck 2018

2 motivation for introducing spatial curvature no longer 750 K] exists in LQC. µ 500 General implications of power suppression at large an- )[

θ 250 ( gles.—In LQC, the mechanism for departure from the C 0 nearly scale invariant ansatz (1) is rooted in fundamen- −250 tal considerations in the Planck regime. Nonetheless, it is natural to ask if the qualitative features of some of our −500 0 25 50 75 100 125 150 175 results will carry over if there were other mechanisms θ that led to the primordial spectrum of the form given in Eq. (2). We now show that this is indeed the case. FIG. 3: The angular power spectrum C(θ). The 2018 Let us then suppose that there is some mechanism that PLANCK spectrum (thick black dots), the LQC [solid (blue) provides a primordial power spectrum of the form (2) for line], and the standard ansatz [dashed (red) line] predic- some k◦. Let us compare and contrast the resulting best tions.Values of cosmological parameters are fixed to the mean fit ΛCDM model with that given by the SA of Eq. (1). values given in Table I. As a first step, let us restrict the analysis only to smaller 4

diverges and reaches its maximum value at the bounce. As a result, preinflationary dynamics naturally inherits a B new scale, kLQC, such that modes with kphys . kLQC at the bounce are not in the BD vacuum at the start of the slow roll phase of inflation [23, 24], whence the primor- dial power spectrum is no longer nearly scale invariant, but of the form (2). The LQC dynamics and initial con- ditions then imply [30] that there is power suppression in CMB at the largest angular scales ℓ . 30. In contrast to other mechanisms that have been proposed, this sup- pression has origin in fundamental, Planck scale physics rather than in phenomenological adjustments put in by hand just before or during the slow roll. As a result of this power suppression, there is an enhancement of op- tical depth τ and suppression of the lensing potential AL. The two together bring the value AL = 1 within 1σ of the LQC τ −AL probability distribution, thereby removing the primary motivation for considering closed universe and the subsequent “potential crisis” [20]. In

FIG. 4: 1σ and 2σ probability distributions in the τ − AL addition, the anomaly in C(θ) at large angles [11–14] is plane. Predictions of the standard ansatz (shown in red) and significantly reduced; the LQC value of S1/2 is ∼ 0.34 LQC (shown in blue). Vertical lines represent the respective of that predicted by standard inflation. The PLANCK τ mean values of . Collaboration had suggested [1] that “. . . if any of the anomalies have primordial origin, then their large scale nature would suggest an explanation rooted in fundamen- angular scales (k ≫ k◦). Then, the primordial spectrum tal physics. Thus it is worth exploring any models that in both schemes is the same, whence we will obtain the might explain an anomaly (even better, multiple anoma- same best fit values of the six cosmological parameters. lies) naturally, or with very few parameters.” In this Denote by A˚ the best fit value of the scalar amplitude s Letter we presented a concrete realization of this idea. A . In the second step, let us bring in the full range of s (For an alternate proposal within LQC see Ref. [40]). observable modes including k ≤ k◦. Now, given the ob- served large-scale suppression in the TT power spectrum, (1) 0.00030 for SA+ΛCDM model the best-fit value As for the en- LQC ] ˚ 2 SA tire k range will be lower than As. By contrast if the 0.00025 primordial power spectrum is of the form of Eq. (2), A˚ µK s [ will not have to be lowered as much to obtain the best fit π 0.00020 (2) 2 A since the initial power is already suppressed by f(k). / s 0.00015 BB (2) (1) ℓ Thus, we have A˚ > As > As . [For the f(k) in LQC, s C 10 10 (2) 0.00010 we have ln(10 A˚s)=3.089 and ln(10 As )=3.054 and ln(1010As(1))=3.044.] The key point is the last + 1)

ℓ 0.00005

(2) (1) ( inequality: As > As . Now, we know that for large ℓ −2τ 0.00000 k, the product Ase is fixed by observations. Hence, 101 102 103 it follows that the best fit values of the optical depth ℓ in the two scheme must satisfy τ (2) > τ (1). Finally, from the very definition of lensing amplitude, the value FIG. 5: Predicted Power spectra for BB polarization with of AL is anticorrelated to the value of As. Therefore, (2) (1) 1σ uncertainty. Comparison between LQC and standard in- we will have A < A . Thus in any theory that has L L flation. The tensor to scalar ratio r has been set to 0.0041, primordial spectrum of the form (2), As, τ, and AL will motivated by Starobinsky inflation [39]. The shaded region have the same qualitative behavior as in LQC, and hence indicates the cosmic variance for SA. the tension with observations would be reduced. What LQC provides is a precise form of the suppression factor This model also leads to other specific predictions. f(k) from “first principles,” and hence specific quanti- First, as Table I shows, the reionization optical depth τ is tative predictions. The LQC f(k) also leads to other predicted to be ∼ 9.8% (i.e., 0.72 σ) higher. This predic- predictions—e.g., for the BB power spectrum discussed tion can be tested by the future observation of global 21 below—that need not be shared by other mechanisms. cm evolution at high redshifts that can reach a percent Summary and discussion.—In LQC, curvature never level accuracy in the measurement of τ [41]. Second, for 5 any given inflationary potential, the primordial spectra tion,” Phys. Rev. D 55, 7368 (1997), [astro-ph/9611125]. of LQC and SA share the same value of r—the tensor to [10] U. Seljak and M. Zaldarriaga, “Signature of gravity waves scalar ratio—which depends on the potential. But there in polarization of the microwave background,” Phys. Rev. 78 is a specific scale dependence in the large-scale B-mode Lett. , 2054 (1997), [astro-ph/9609169]. [11] D. N. Spergel et al. [WMAP Collaboration], “First year (odd-parity) polarization power spectrum, as shown in Wilkinson Microwave Anisotropy Probe (WMAP) obser- Fig. 5. The difference is driven by the LQC suppression of vations: Determination of cosmological parameters,” As- the primordial tensor amplitude combined with the larger trophys. J. Suppl. 148, 175 (2003), [astro-ph/0302209]. reionization contribution due to higher τ. Provided that [12] D. Sarkar, D. Huterer, C. J. Copi, G. D. Starkman and r is sufficiently large, for example, r & 0.001, we may D. J. Schwarz, “Missing power vs low-l alignments in be able to test this prediction against the data from the the cosmic microwave background: No correlation in the 34 future B-mode missions such as LiteBIRD [42], Cosmic standard cosmological model,” Astropart. Phys. , 591 (2011), [arXiv:1004.3784 [astro-ph.CO]]. Origins Explorer [43], or Probe Inflation and Cosmic Ori- et al. BB [13] Y. Akrami [Planck Collaboration], “Planck 2018 gins (PICO [44]). Again, LQC modifies Cℓ on large results. VII. Isotropy and statistics of the CMB,” scales where the cosmic variance limits its detectability. arXiv:1906.02552 [astro-ph.CO]. However, in light of results presented in this Letter, we [14] D. J. Schwarz, C. J. Copi, D. Huterer and G. D. Stark- hope that the LQC primordial power spectrum will be man, “CMB anomalies after Planck,” Class. Quant. included in the future cosmological analysis. Grav. 33, no. 18, 184001 (2016), [arXiv:1510.07929 [astro-ph.CO]]. We would like to thank Ivan Agullo and Charles [15] P. Motloch and W. Hu, “Tensions between direct mea- Lawrence for valuable inputs and Pawel Bielewicz for surements of the lens power spectrum from Planck data,” Phys. Rev. D 97, no. 10, 103536 (2018), help with Fig. 3. This work was supported in part [arXiv:1803.11526 [astro-ph.CO]]. by the NSF Grants No. PHY-1505411 and No. PHY- [16] F. Couchot, S. Henrot-Versill, O. Perdereau, 1806356, the NASA ATP Grant No. 80NSSC18K1103, S. Plaszczynski, B. Rouill d’Orfeuil, M. Spinelli and the Eberly research funds of Penn State. V.S. was and M. Tristram, “Relieving tensions related to the supported by the Inter-University Centre for Astronomy lensing of the cosmic microwave background temperature 597 and Astrophysics, Pune during the early stages of this power spectra,” Astron. Astrophys. , A126 (2017) work. Portions of this research was conducted with high doi:10.1051/0004-6361/201527740 [arXiv:1510.07600 [astro-ph.CO]]. performance computing resources provided by Louisiana [17] P. Motloch and W. Hu, “Lensinglike tensions in State University [45]. the P lanck legacy release,” Phys. Rev. D 101, no.8, 083515 (2020) doi:10.1103/PhysRevD.101.083515 [arXiv:1912.06601 [astro-ph.CO]]. [18] G. Addison, Y. Huang, D. Watts, C. Bennett, M. Halpern, G. Hinshaw and J. Weiland, “Quantify- [1] Y. Akrami et al. [Planck Collaboration], “Planck 2018 re- ing discordance in the 2015 Planck CMB spectrum,” sults. I. Overview and the cosmological legacy of Planck”, Astrophys. J. 818, no.2, 132 (2016) doi:10.3847/0004- arXiv:1807.06205 [astro-ph.CO]. 637X/818/2/132 [arXiv:1511.00055 [astro-ph.CO]]. [2] R. Adam et al. [Planck Collaboration], “Planck interme- [19] W. Hadley, Curvature tension: evidence for a closed diate results. XLVII. Planck constraints on reionization universe,[arXiv:1908.09139 [astoph-CO]]. history,” Astronomy & Astrophysics. 596, A108 (2016). [20] E. Di Valentino, A. Melchiorri and J. Silk, “Planck evi- [3] U. Seljak and M. Zaldarriaga, “A Line of sight integration dence for a closed Universe and a possible crisis for cos- approach to cosmic microwave background anisotropies,” mology,” Nat. Astron. (2019) [arXiv:1911.02087 [astro- Astrophys. J. 469, 437 (1996), [astro-ph/9603033]. ph.CO]]. [4] A. Lewis, A. Challinor and A. Lasenby, “Efficient com- [21] A. Ashtekar and P. Singh, “Loop quantum cosmology: A putation of CMB anisotropies in closed FRW models,” status report,” Class. Quant. Grav. 28, 213001 (2011), Astrophys. J. 538, 473 (2000), [astro-ph/9911177]; [arXiv:1108.0893 [gr-qc]]. [5] D. Blas, J. Lesgourgues and T. Tram, “The Cosmic Lin- [22] I. Agullo and P. Singh, In Loop Quantum Gravity: The ear Anisotropy Solving System (CLASS) II: Approxima- first 30 years, edited by A. Ashtekar and J. Pullin, (World tion schemes,” JCAP 1107 (2011) 034, [arXiv:1104.2933 Scientific, Singapore, 2017), [arXiv:1612.01236 [gr-qc]]. [astro-ph.CO]]. [23] I. Agullo, A. Ashtekar and W. Nelson, “A quantum grav- [6] N. Aghanim et al. [Planck Collaboration], “Planck ity extension of the inflationary scenario,” Phys. Rev. 2018 results. V. CMB power spectra and likelihoods,” Lett. 109, 251301 (2012), [arXiv:1209.1609 [gr-qc]]. arXiv:1907.12875 [astro-ph.CO]. [24] I. Agullo, A. Ashtekar and W. Nelson, “The pre- [7] N. Aghanim et al. [Planck Collaboration], “Planck 2018 inflationary dynamics of loop quantum cosmology: Con- results. VI. Cosmological parameters,” [arXiv:1807.06209 fronting quantum gravity with observations,” Class. [astro-ph.CO]]. Quant. Grav. 30, 085014 (2013), [arXiv:1302.0254 [gr- [8] W. Hu and T. Okamoto, “Mass reconstruction with qc]]. cmb polarization,” Astrophys. J. 574, 566 (2002), [25] M. Fernandez-Mendez, G. A. Mena Marugan, and [astro-ph/0111606]. J. Olmedo, “Hybrid quantization of an inflation- [9] M. Kamionkowski, A. Kosowsky and A. Stebbins, ary universe,” Phys. Rev. D 86, 024003 (2012), “Statistics of cosmic microwave background polariza- [arXiv:1205.1917[gr-qc]]. 6

[26] A. Barrau, T. Cailleteau, J. Grain, and J. Mielczarek, ulated creation of quanta in the inflationary universe,” “Observational issues in loop quantum cosmology,” Phys. Rev. D 83, 063526 (2011) [arXiv:1010.5766 [astro- Class. Quant. Grav. 31 (2014) 053001, [ arXiv:1309.6896 ph.CO]]. [gr-qc]]. [36] J. Ganc and E. Komatsu, Scale-dependent bias of galax- [27] A. Ashtekar and A. Barrau, “Loop quantum cosmology: ies and mu-type distortion of the cosmic microwave back- From pre-inflationary dynamics to observations,” Class. ground spectrum from single-field inflation with a modi- Quant. Grav. 32, 234001 (2015), [arXiv:1504.07559 [gr- fied initial state, Phys. Rev. D 86, 023518 (2012) [arXiv: qc]]. 1204.4241 [astro-ph.CO]] [28] I. Agullo and N. A. Morris, “Detailed analysis of the [37] R. Penrose, “The Road to Reality (section 28.8),” Alfred predictions of loop quantum cosmology for the primor- A Knopf, NY, 2004. dial power spectra,” Phys. Rev. D 92, 124040 (2015), [38] A. Bhardwaj, E. J. Copeland, J. Louko, “Inflation in [arXiv:1509.05693 [gr-qc]]. Loop Quantum Cosmology,” Phys. Rev. D99, 063520 [29] I. Agullo, “Loop quantum cosmology, non-Gaussianity, (2019) [arXiv:1812.06841 [gr-qc]]. and CMB power asymmetry,” Phys. Rev. D 92, 064038 [39] A. A. Starobinsky, “A new type of isotropic cosmolog- (2015) arXiv:1507.04703. ical models without singularity,” Phys. Lett. 91B, 99 [30] A. Ashtekar and B. Gupt, “Quantum gravity in the (1980) [Adv. Ser. Astrophys. Cosmol. 3, 130 (1987)]. sky: Interplay between fundamental theory and ob- doi:10.1016/0370-2693(80)90670-X servations,” Class. Quant. Grav. 34, 014002 (2017), [40] I. Agullo, D. Kranas and V. Sreenath, Anomalies in the [arXiv:1608.04228 [gr-qc]]. CMB from a cosmic bounce, [2005.01796 [astro-ph.CO]]. [31] A. Ashtekar and B. Gupt, “Initial conditions for cosmo- [41] A. Fialkov and A. Loeb, “Precise Measurement of the logical perturbations,” Class. Quant. Grav. 34, 035004 Reionization Optical Depth from The Global 21-cm (2017), [arXiv:1610.09424 [gr-qc]]. Signal Accounting for Cosmic Heating,” Astrophys. J. [32] L. C. Gomar, G. A. Mena-Marugan, D. M. De Blas, and 821, no. 1, 59 (2016) doi:10.3847/0004-637X/821/1/59 J. Olmedo, “Hybrid loop quantum cosmology and predic- [arXiv:1601.03058 [astro-ph.CO]]. tions for the cosmic microwave background,” Phys. Rev. [42] T. Matsumura et al., “Mission design of LiteBIRD,” D96, 103528 (2017), [arXiv:1702.06036 [gr-qc]]. J. Low. Temp. Phys. 176, 733 (2014) [arXiv:1311.2847 [33] I. Agullo, B. Bolliet and V. Sreenath, “Non-Gaussianity [astro-ph.IM]]. in loop quantum cosmology,” Phys. Rev. D97, 066021 [43] J. Delabrouille et. al. [CORE Collaboration] “Exploring (2018), [arXiv:1712.08148 [gr-qc]]. cosmic origins with CORE: Survey requirements and mis- [34] V. Sreenath, I. Agullo and B. Bolliet, “Computation of sion design” JCAP, 2018, 04, 014 (2018). non-Gaussiantity in loop quantum cosmology,” arXiv: [44] S. Hanany et al. [NASA PICO Collaboration], 1904.01075 [gr-qc]. “PICO: Probe of Inflation and Cosmic Origins,” [35] I. Agullo and L. Parker, “Stimulated creation of quanta arXiv:1902.10541 [astro-ph.IM]. during inflation and the observable universe,” Gen. Rel. [45] http://www.hpc.lsu.edu. Grav. 43, 2541 (2011) [arXiv:1106.4240 [astro-ph.CO]]; I. Agullo and L. Parker, “Non-gaussianities and the Stim-