PHYSICAL REVIEW D 101, 023519 (2020)

Minimal signatures of the in non-Gaussianities

Anson Hook* Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA † ‡ Junwu Huang and Davide Racco Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

(Received 19 September 2019; published 22 January 2020)

We show that the leading coupling between a shift symmetric inflaton and the standard model fermions leads to an induced electroweak symmetry breaking due to particle production during inflation, and as a result, a unique oscillating feature in non-Gaussianities. In this one parameter model, the enhanced production of standard model fermions dynamically generates a new electroweak symmetry breaking minimum, where the Higgs field classically rolls to. The production of fermions stops when the Higgs expectation value and hence the fermion masses become too large, suppressing fermion production. The balance between the above-mentioned effects gives the standard model fermions masses that are uniquely determined by their couplings to the inflaton. In particular, the heaviest standard model fermion, the top , can produce a distinct cosmological collider physics signature characterized by a one-to-one relation between amplitude and frequency of the oscillating signal, which is observable at future 21-cm surveys.

DOI: 10.1103/PhysRevD.101.023519

I. INTRODUCTION AND SUMMARY induces electroweak symmetry breaking during inflation, whereas a large expectation value of the Higgs field Cosmological collider physics [1–8] provides an oppor- increases the masses of the SM fermions and suppresses tunity to search for new heavy particles that are not their production. This interplay results in a very predictive accessible at particle colliders. These heavy particles, scenario where the strength of the oscillating signature in produced through their interactions with the inflaton field, non-Gaussianities is directly tied to the period of oscillation. can accumulate to large enough densities and affect the We assume that the fermions in the SM couple to the bispectrum of density perturbations, leaving observable inflaton through the lowest dimensional operator respecting signatures in the cosmic microwave background and large the shift symmetry of the inflaton [11,12], scale structure of the Universe [9,10]. Given the exciting potential of this approach, it is worth ∂ ϕ “ L ⊃ μ F†σ¯ μF fc†σ¯ μfc y HFfc; asking What are the minimal signatures of the standard Λ ð þ Þþ f ð1Þ model (SM) in the context of cosmological collider phys- f ics?” Of course the absolutely minimal signature is nothing v h where ϕ is the inflaton, H 0; pþffiffi is the Higgs doublet, if the SM does not couple directly to the inflaton. In this ¼ð 2 Þ and F Q, L and fc uc;dc;ec are left- and right-handed article, we explore the consequences of adding a single ¼ ¼ fermions in the SM in two-component notation.1 When coupling to the SM fermions, the dimension five shift ϕ_ ≠ 0 symmetric coupling between the inflaton and the SM h i , this coupling leads to the production of fermions during inflation whose effective number density is nf ∼ fermions. Somewhat surprisingly, this single coupling by ffiffiffi 2 2 ϕ_ p itself leads to an interplay between the dynamics of the SM mfλ exp −πm =λfH , where λf , mf yfv= 2, H is f ½ f ¼ Λf ¼ fermions and the Higgs: The SM fermion production pffiffiffi the Hubble parameter during inflation, and v= 2 ¼hHi is the vacuum expectation value (vev) of the Higgs field. It is well known that a high density of particles can *[email protected] † [email protected] change the properties of a scalar potential. Thermal effects ‡ [email protected] favor symmetry restoration of the Higgs for temperatures above the electroweak phase transition [13]. On the other Published by the American Physical Society under the terms of hand, chemical potentials favor symmetry breaking and in the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, 1We neglect the typically smaller dimension five anomalous and DOI. Funded by SCOAP3. couplings to the gauge bosons.

2470-0010=2020=101(2)=023519(6) 023519-1 Published by the American Physical Society ANSON HOOK, JUNWU HUANG, and DAVIDE RACCO PHYS. REV. D 101, 023519 (2020) the context of the Higgs potential could prevent symmetry restoration even at high temperatures [14]. The coupling in Eq. (1) is very similar to a chemical potential. In fact, if the plus sign were a minus, it would be the familiar chemical potential for fermion number. As such, it is unsurprising to find that the effect of this coupling is to generate a correction to the Higgs potential that favors symmetry breaking of the form   y2 πy2h2 δV − f λ2h2 − f : FIG. 2. Contribution to the inflaton bispectrum from a loop of h ¼ 2 f exp ð2Þ f τ 2π 2λfH SM fermions. Two fermions are produced at a time 3 by the interaction with a soft inflaton leg δϕ, and annihilate later at τ1 ∼ τ2 into two hard inflaton legs with k1, k2 ≫ k3. The For λf >H≫ v (v being the electroweak vacuum), EW EW nonanalytic contribution to the bispectrum is due to the time this contribution to the potential induces spontaneous break- propagation of the fermions from τ3 to τ1, τ2. ing of the electroweak symmetry, as shown in Fig. 1. However, as the Higgs vev increases, the fermion masses increase and their particle production is exponentially sup- solely determined by the inflaton coupling λf to that 2 pressed as mf ≳ λfH. Therefore, quite insensitively to any fermion. As a result, the non-Gaussian signal in the other term of the Higgs potential, e.g., the value of the quartic squeezed limit simplifies into λh, the Higgs gets a vev during inflation: pffiffiffi 4 2N P qffiffiffiffiffiffiffiffiffi fðclockÞ ≈ c ζ λ˜13=2; 1 NL 3e f ð4Þ v ∼ λfH: ð3Þ yf depending only on the size of the inflaton fermion coupling _ ˜ λf ϕ in Hubble units λf . This signal oscillates in In the SM, due to the large hierarchy between the ¼ H ¼ ΛfH ˜ and the lighter leptons and , this effect is determined lnðk3=k1Þ with a frequency ∼λf in the squeezed limit. This entirely by the top quark. Incidentally, such a scenario can relation between the amplitude (fðclockÞ) and the frequency only occur for fermions with an Oð1Þ Yukawa coupling, NL ˜ of the oscillating signal offers a simple cross-check of this since λf ¼ λf=H cannot be arbitrarily large. Thus, in what mechanism. Such a signature offers a direct probe of the follows, we focus on the coupling of the top quark with the induced electroweak symmetry breaking during inflation, inflaton. and could help us to shed light on the inflationary sector. The observational signature associated to this coupling is the generation of a large non-Gaussian oscillating pattern in the squeezed limit. The Feynman diagram to be calculated II. PARTICLE PRODUCTION AND is shown in Fig. 2 [11,12]. THE HIGGS POTENTIAL The interesting feature in this case is that the dynamics of In this section, we discuss particle production and how the Higgs potential ensures that the mass of the fermion f the fermion density affects the Higgs potential. To calculate that produces the largest observable non-Gaussianity is the correction to the Higgs mass term, we calculate the diagram shown in Fig. 3 that corrects the energy density of the state. In a companion paper [12] (see in particular Sec. III and Appendix A), we show in detail how to estimate and calculate these diagrams. For a single fermion flavor and color, the diagrams in Fig. 3 contribute as ZZ 0 τ τ 2 αβ α_ β_ d 1 d 2 ⃗ ⃗ Nab ¼ −yfϵ ϵ ab Gaðk1; τ1ÞGbð−k1; τ2Þ −∞ Hτ Hτ Z 1 2 d3q × ðD _ ðp⃗12; τ1; τ2ÞDabβα_ ð−p⃗21; τ1; τ2Þ ð2πÞ3 abαβ

þ Dbaαβ_ ð−p⃗12; τ2; τ1ÞDbaβα_ ðp⃗21; τ2; τ1ÞÞ; ð5Þ FIG. 1. Higgs potential at zero temperature and λf ∼ 0 (blue line) and in the presence of a top quark condensate induced by ⃗ where τ denotes conformal time, p⃗12 k1 p⃗21 q⃗ λt >H>v (purple line). The Higgs field sits in the dynami- ¼ þ ¼ EW ⃗ cally generated minimum v during inflation. and jq⃗j ≫ jk1j is the internal momentum. The indices

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α; β; α_; β_ ∈ f1; 2g are spinor indices. The antisymmetric ϵ 12 tensors are defined by ϵ ¼−ϵ12 ¼1. The in-in indices a; b take values in fþ1; −1g, denoted respectively by f⊕; ⊖g to distinguishpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi them from spinor indices. The functions ⃗ 2 3 iakτ ⃗ Gaðk;τÞ¼ H =2k ð1−iakτÞe and Dabαβ_ ðk; τ1; τ2Þ are the propagator of the Higgs and the fermion fields respectively (see Sec. A.2 of [12]). By the same logic of FIG. 3. Feynman diagrams for the contribution of the top the electroweak , the momentum integral fermion condensate to the Higgs potential. For notations, see the in Eq. (5) is quadratically divergent. The leading quadratic main text and [12,15,16]. divergence is absorbed into the definition of the physical Higgs mass that we observe today when λf ¼ 0 (this the Higgs potential to the exponential suppression of the operation automatically removes some of the subleading 3 ˜ fermion density. corrections in the λf expansion). In the massless limit, the There is not a clean analytic formula interpolating integral in Eq. (5) can be simplified (by exploiting proper- between the small and large mass regions and a full result ties of the Whittaker functions appearing in the fermion would need to be obtained numerically. For simplicity, we mode functions) to be interpolate between the two expressions using the follow- Z 3 ZZ ing potential: d q dτ1 dτ2 2 −iaðp12þp21Þðτ2−τ1Þ Naa ¼y 2θðτ2 −τ1Þe f 2π 3 Hτ Hτ 2  2 2 ð Þ 1 2 Ncy πy jHj      V −μ2 H 2 λ H 4 − f λ2 H 2 − f ; ˜ ˜ h ¼ hj j þ hj j 2 fj j exp τ 2iλf τ 2iλf π λ H 1 2 G k⃗;τ G −k⃗;τ ; f × τ þ τ að 1 1Þ að 1 2Þþ 2 1 ð9Þ ð6Þ up to corrections that are independent of λf, where μh and a b λh are the coefficients of the quadratic and quartic terms of where we only consider the terms where ¼ . The terms pffiffiffi with a ≠ b are not divergent, related to the fact that the the Higgs potential, and mh ¼ 2μh is the physical mass of counterterm δm2h2=2 for the Higgs mass can only cancel the . 2 2 the divergences in δm⊕⊕ (N⊕⊕) and δm⊖⊖ (N⊖⊖). Moreover, these two counterterms are related by a minus III. NON-GAUSSIAN SIGNATURE sign (due to complex conjugation). As a result, we find the The induced Higgs potential in Eq. (9) has a new correction to the Higgs potential from the diagrams in minimum at Fig. 3 by taking the difference between the two diagrams, rffiffiffiffiffiffiffiffiffiffiffiffi  removing in this way the corrections that are linearly 1 2 eπλ =y4 v λ H 1 − h f O λ2 ; divergent [15]: ¼ f ˜ þ ð hÞ ð10Þ yf π NCλf 2 2 2 2 2 δm 1 δm⊕⊕ − δm⊖⊖ yfλf − : for v ≫ v . In the SM, the top quark Yukawa is yt ¼ 3 ¼ 3 2 ¼ 2 3 ð7Þ pffiffiffi EW 3k 3k 3π k 2m =v ≈ 1 t EW at the weak scale and runs to about 0.6 at λ m2=2v2 ≈ 0 13 This gives the correction from a single massless fermion high energies, while the quartic is h ¼ h EW . at flavor/color to the Higgs potential the weak scale and runs to jλhj ≲ 0.02 at high energies. This ensures that the small quartic expansion is a good approxi- y2 mation for λf=H ≫ 1. δV − f λ2h2 h ¼ 2π2 f ð8Þ In [12], we discuss in detail how to compute the nonanalytic signal induced in the bispectrum by fermions ˜ 2 at leading order in the large λf expansion and to leading interacting with the inflaton. The result in the squeezed λ˜ order in the Higgs field. limit and at leading order in the large f expansion is In the large mf limit, we obtain an exponential sup-   ˜ 2−2iλf 2 2 k3≪k1∼k2 ðclockÞ k3 pression with exponent ∼−yfh =λfH. We cannot calcu- S k ;k ;k ≃ f ; ð 1 2 3Þ NL k ð11Þ late the coefficient of the exponent. As an approximation, 1 we match this exponential suppression for the correction to 3We acknowledge the potential existence of subleading terms m =H 2In the massless limit, the potential can be computed to next-to- in the small f limit due to our inability to resum and y2 reproduce the exact exponential suppression in the fermion λ˜ δV − f λ2 − H2 h2 leading-order in large f expansion to be h ¼ 2π2 ð f 2 Þ . density.

023519-3 ANSON HOOK, JUNWU HUANG, and DAVIDE RACCO PHYS. REV. D 101, 023519 (2020) pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where mf ¼ λfH=π ≪ λf, and   N m 3 fðclockÞ ≈ c P −1=2 f λ˜2 NL ζ f 6π Λf ˜ eπλf μ˜ Γ −iμ˜ 2Γ 2iμ˜ 3 f ð fÞ ð fÞ ; · ˜ 3 ˜ ð12Þ 2πΓðiðλf þ μ˜ fÞÞ Γðiðμ˜ f − λfÞþ1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 where μf ¼ λf þ mf and μ˜ f ¼ μf=H. In the scenario discussed in this paper, the contribution to the Higgs potential from the top quark condensatepffiffiffiffiffiffiffiffiffiffiffiffiffiffidynamically adjusts the Higgs vev so that mf ¼ λfH=π, and the f nonanalytic contribution to the bispectrum is just a function FIG. 4. Size of NL generated by the top quark condensate in λ˜ the scenario described in this paper [Eq. (13)], as a function of of f: _ _ 2 λt=H ¼ ctϕ=ΛfH (or ϕ=Λf, assuming ct ¼ 1). pffiffiffi 4 2N P fðclockÞ ≈ c ζ λ˜13=2: to distinguish the scenario that we describe in this paper NL f ð13Þ 3e from other models generating this feature. Surprisingly, high energy colliders probing the flavor We show the contribution to f from the top quark in our NL structure of the SM [21] provide an alternative route for scenario as a function of λt=H in Fig. 4. Until now, we have testing our scenario. For a typical slow-roll inflation not specified whether the quartic coupling λh of the Higgs model [22–25], the inflaton mass m is5 field is positive or negative. In the SM, it is known [17–19] inf that, for the central measured values of the SM parameters, λ 1011 λ m ≪ H ≲ 10−2Λ ; h turns negative around GeV. If h is positive at the inf inf f ð14Þ scale of the dynamically generated minimum v, then we have the clean signal shown in Fig. 4. If instead λh is where the last inequality comes from the requirement negative at that scale, some additional UV contribution −1=2 −1=4 Pζ H Pζ ϕ_ 1=2 2 λ˜ pffiffiffiffi ϕ_ ≲ Λ needs to be added to stabilize the potential at high energies that f ¼ 2π Λ ¼ 2π ðΛ2 Þ satisfies f so that v f f and generate a high scale minimum UV [12]. In the latter we can rely on the effective field theory expansion in case, the dynamically generated minimum can either over- Λf BABAR v powers of . Experimental constraints from and come the one at UV, yielding only one Higgs minimum exotic meson decays imply a bound Λf ≳ 10 TeV for located close to v, or coexist with it, giving rise to a two- scalars that couple with “Yukawa-like couplings” to the minima potential. If the two minima coexist, the Higgs field three generations of SM fermions taking into account the could have lived in either of the two minima during 4 relation between the mass and the coupling of the inflaton inflation. Depending on whether the Higgs field sat in (see Secs. 4.1 and 4.2 in [21] and also [26,27] for more the dynamical minimum or in the high scale minimum v , UV details). A detailed study of the flavor signatures of this the signature could come respectively from the top quark scenario is beyond the scope of this paper. through the mechanism discussed here, or from one of the A potentially observable signal in future measurements other SM fermions [12] (see Fig. 5). f ≳ 10 λ˜ of the bispectrum (say NL ) requires a large f, which together with Λf ≳ 10 TeV translates to a lower bound on IV. REMARKS the Higgs vev during inflation: In this article, we described the signatures of shift rffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi symmetric couplings between the inflaton and the SM, 1 2λ H 8π v ≈ f ≈ λ˜3=2P 1=2Λ ≳ 300 : in particular the one to the top quark. This coupling y π y f ζ f GeV ð15Þ dynamically sets the masses of the SM fermions and t t simultaneously determines the strength of the non- Gaussianity giving rise to the unique feature that the Similarly to the correction to the Higgs vev duringp inflationffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k =k λ v ≡ m2=2λ frequency of the oscillating pattern in lnð 3 1Þ fixes the from h, there is also a correction from EW h h λ ∼ v amplitude of the non-Gaussian signal. This provides a way when f EW. Such a correction amounts to an expansion

4 We notice that the Higgs squared mass evaluated at v is larger 5We assume for simplicity a scenario where the inflaton mass 9 H2 λ˜ ≳ 7 than 4 for t : in this range, the Higgs field is not subject to today does not differ too much from the inflaton mass minf during quantum fluctuations in v. inflation.

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2 2 mass term [like the term −μhjHj in Eq. (9)] can lead to corrections to the Higgs vev v during inflation. Requiring

that Eq. (16) is a negligible correction to v implies c2 ≲ N y2 c t ≈ 0 1 Λ Λ c π2e . if f ¼ H.If 2 is large and positive, the minima in the Higgs potential would disappear (together with the signal), while if c2 is large and negative, then we go back to the cases studied in [6,12], where the Higgs vev is not dynamically adjusted by the mechanism discussed here. Finally, the backreaction of the fermion density on the inflaton dynamics is negligible [12]. The signature that we discuss can also arise whenever there is a fermion whose mass is generated from an Oð1Þ FIG. 5. Parameter space where the signal described in this paper Yukawa coupling. For example, if the dark sector contains ˜ and in [12] can appear for λt ¼ 30. The horizontal axis (scale dark fermions whose mass is generated (also partially) from v UV) is the would-be location of the high energy minimum of the Yukawa couplings to a dark Higgs boson, then the leading Higgs potential determined by a negative quartic coupling and a order shift symmetric couplings between the dark fermions H 6=Λ2 positive j j H operator. The thin black vertical lines mark the and the inflaton would result in a signal similar to the one λ scale at which h becomes negative. The blue lines separate we discuss (with a different Nc). regions where only a dynamical minimum v exists from regions Soon, the limits on non-Gaussianities and the scalar-to- where two minima can coexist. In the blue shaded region there is tensor ratio will improve dramatically [9,10,28,29].Itis only one dynamical minimum and the signal from the top quark v thus extremely interesting to ask what sort of signals might can be observable. Below the blue lines, the two minima UV and v coexist and detectable signatures can come from either. In the be discovered in the upcoming years. In this article, we green shaded region, the signal from the other SM fermions [12] described the most minimal way in which the SM itself f ≳ 1 can be observable with NL . Above the orange line, the may reappear in the sky. In the near future, a combination dimension 6 Higgs operator becomes strongly coupled and of flavor measurements at particle colliders and bispectrum additional information on the Higgs potential is needed to measurements at the cosmological collider may combine to determine the signal properties. The gray shaded region is uncover deep mysteries of the Universe. excluded by measurements of the tensor-to-scalar ratio. Below the violet dashed line the Higgs field would have not been brought back to the electroweak minimum by thermal effects ACKNOWLEDGMENTS v during reheating, if it was sitting in UV during inflation. The We would like to acknowledge Asimina Arvanitaki black, orange and blue lines are solid or dashed depending on for relentlessly inviting us to think about this scenario. whether the running of λh is extrapolated using the central value of the top mass or a þ2σ deviation [20]. We also thank Prateek Agrawal, David Curtin, Savas Dimopoulos, Jiji Fan, Daniel Egaña-Ugrinovic, Matthew

v2 Johnson, Soubhik Kumar, Gustavo Marques-Tavares, EW eπλh in 2 4 ˜ , which is also a small correction as long as Maxim Pospelov, Antonio Riotto, Raman Sundrum, and v yt Ncλf v ≳ v Zhong-Zhi Xianyu for many useful discussions. J. H. and EW. A potentially significant correction to the scenario we D. R. thank the Stanford Institute for Theoretical Physics, have described can arise if there is a significant coupling and A. H. and J. H. thank MIAPP and KITP Santa Barbara, between the inflaton and the Higgs boson in the form of for generous hospitality during the completion of this work.   This research was supported in part by Perimeter Institute 2 ∂ϕ † for Theoretical Physics. Research at Perimeter Institute is c2 H H: ð16Þ ΛH supported in part by the Government of Canada through the Department of Innovation, Science and Economic This coupling can be generated from UV dynamics or by Development Canada and by the Province of Ontario integrating out SM fermions that couple directly to the through the Ministry of Economic Development, Job inflaton. In order for the scenario described in this paper to Creation and Trade. A. H. is supported in part by the follow through, we needed to be able to suppress any large NSF under Grant No. PHY-1620074 and by the Maryland corrections to the Higgs mass. During inflation, Eq. (16) Center for Fundamental Physics (MCFP). This research _ 2 leads to a Higgs mass term of order c2ðϕ=ΛHÞ , potentially was supported in part by the National Science Foundation comparable to the mass term shown in Eq. (10). This under Grant No. NSF PHY-1748958.

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[1] X. Chen and Y. Wang, J. Cosmol. Astropart. Phys. 04 [18] G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. (2010) 027. Giudice, G. Isidori, and A. Strumia, J. High Energy Phys. 08 [2] D. Baumann and D. Green, Phys. Rev. D 85, 103520 (2012). (2012) 098. [3] N. Arkani-Hamed and J. Maldacena, arXiv:1503.08043. [19] D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. [4] H. Lee, D. Baumann, and G. L. Pimentel, J. High Energy Sala, A. Salvio, and A. Strumia, J. High Energy Phys. 12 Phys. 12 (2016) 040. (2013) 089. [5] X. Chen, Y. Wang, and Z.-Z. Xianyu, J. High Energy Phys. [20] G. Franciolini, G. F. Giudice, D. Racco, and A. Riotto, 04 (2017) 058. J. Cosmol. Astropart. Phys. 05 (2019) 022. [6] S. Kumar and R. Sundrum, J. High Energy Phys. 05 (2018) [21] M. J. Dolan, F. Kahlhoefer, C. McCabe, and K. Schmidt- 011. Hoberg, J. High Energy Phys. 03 (2015) 171; 07 (2015) 103 [7] S. Alexander, S. J. Gates, L. Jenks, K. Koutrolikos, and E. (E). McDonough, J. High Energy Phys. 10 (2019) 156. [22] A. H. Guth, Phys. Rev. D 23, 347 (1981); Adv. Ser. [8] S. Lu, Y. Wang, and Z.-Z. Xianyu, arXiv:1907.07390. Astrophys. Cosmol. 3, 139 (1987). [9] J. B. Muñoz, Y. Ali-Haïmoud, and M. Kamionkowski, Phys. [23] A. D. Linde, Phys. Lett. 108B, 389 (1982); Adv. Ser. Rev. D 92, 083508 (2015). Astrophys. Cosmol. 3, 149 (1987). [10] P. D. Meerburg, M. Münchmeyer, J. B. Muñoz, and X. [24] D. H. Lyth and A. Riotto, Phys. Rep. 314, 1 (1999). Chen, J. Cosmol. Astropart. Phys. 03 (2017) 050. [25] D. Baumann, Physics of the Large and the Small, TASI 09, in [11] X. Chen, Y. Wang, and Z.-Z. Xianyu, J. High Energy Phys. Proceedings of the Theoretical Advanced Study Institute in 09 (2018) 022. Elementary , Boulder, Colorado, 2009 [12] A. Hook, J. Huang, and D. Racco, arXiv:1907.10624. (World Scientific, Singapore, 2011), pp. 523–686, https:// [13] A. D. Linde, Contemp. Concepts Phys. 5, 1 (1990); arXiv: www.worldscientific.com/doi/abs/10.1142/9789814327183_ hep-th/0503203. 0010. [14] K. M. Benson, J. Bernstein, and S. Dodelson, Phys. Rev. D [26] B. Döbrich, F. Ertas, F. Kahlhoefer, and T. Spadaro, Phys. 44, 2480 (1991). Lett. B 790, 537 (2019). [15] X. Chen, Y. Wang, and Z.-Z. Xianyu, J. High Energy Phys. [27] J. Beacham et al., J. Phys. G 47, 010501 (2020). 08 (2016) 051. [28] K. N. Abazajian et al. (CMB-S4 Collaboration), arXiv: [16] X. Chen, Y. Wang, and Z.-Z. Xianyu, J. Cosmol. Astropart. 1610.02743. Phys. 12 (2017) 006. [29] S. Shandera, N. Dalal, and D. Huterer, J. Cosmol. Astropart. [17] J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, Phys. 03 (2011) 017. A. Riotto, and A. Strumia, Phys. Lett. B 709, 222 (2012).

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