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PoS(HEASA2018)022 https://pos.sissa.it/ † , Geoff Beck and Sergio Colafrancesco ∗ [email protected] Speaker. In memory of Professor Sergio Colafrancesco who sadly passed away before this work was completed. The events observed by LIGO indicateblack holes. the This existence unexpected of result a lead to largeof a population primordial resurgence black in of the holes intermediate interest with mass in several theories studiessatisfy of showing the the that formation broad stringent mass constraints distributions on canthey evade monochromatic provide or populations. the perfect If test-bed such forblack large theories hole populations beyond evolution. exist the The standard case modelof we the of studied black physics hole is that evolution that modify where of itdetermine "Planck explodes what via ", the quantum a high-frequency loop hypothetical background modification signal motivatedof tunnelling. of cosmic such We history objects would exploding over lookconstraints the like on whole for quantum loop various gravity black viathe hole comparison same populations to observed frequencies. to isotropic place background We actualreleased signals find at empirical via that the stringent high-energy constraints channel,signal heavily thereby could restrict result casting in the doubt gamma-ray amount on bursts as of whether speculated or energy in not the literature. the high-energy † ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). High Energy Astrophysics in Southern Africa1-3 - August, HEASA2018 2018 Parys, Free State, South Africa School of Physics, University of theSouth Witwatersrand, Africa Private Bag 3, WITS-2050, Johannesburg, E-mail: Justine Tarrant Probing quantum gravity using high-energy astrophysics PoS(HEASA2018)022 ], 10 6 , ∼ 2 , 5 ] (mean mass Justine Tarrant ]. Black holes 15 10 , ]. 9 [ 19 ], this mass range be- ] for example). These ,

17 15 M 18 , 7 , − ], renewed interest in more 14 17 , 21 16 ] prevent these primordial black 13 Hubble times for a black 50 ]. Therefore, finding ways to probe quantum 4 , 3 1 ]. , 6 2 ]. The use of the lognormal mass distributions is impor- 24 ]. Whilst early research considered primordial black holes , 12 23 , 22 ], but due to the large relativistic , the bounce appears to ] a LIGO relevant mass range is considered instead (mean mass 2 ] shows that if an extended mass distribution is used instead, then these 14 14 ] - a process that takes up to 10 8 would not be exploding in the present epoch, therefore if we are to observe ]. This is because it is very difficult to observe the quantum effects of gravity

2 , M 7 1 − ]. However, [ ) where the relevant limits arise from Kepler microlensing data [ ], takes place much faster. The bounce and tunnelling occur very rapidly in the rest-frame 20

9 M ]. As a result, is not a cosmologically significant mechanism. A Planck 9 6 − We consider two cases that both assume lognormal mass distributions: that of [ Black holes are known to be stable in classical general relativity. However, they may decay Building a consistent quantum theory of gravity is challenging, especially when it comes down The formation of primordial black holes in the very early universe has been widely discussed ). The constraints from millilensing of limit the primordial black holes to constitute ]. Due to their size they interact weakly with other massive bodies and have therefore been 10 ], it stops collapsing and ‘bounces’ due to a quantum pressure not unlike the pressure preventing

11 7 massive primordial black holes [ tant as they have been shown to approximately model the seeding of primordial density constraints are relaxed sufficiently to allowcosmological the primordial dark black matter. holes to account This for has, practically when all combined with LIGO [ hole [ which were smaller thanholes a from solar making mass, up stringent aextended constraints mass large distributions [ fraction may of weaken the dark constraintsThe matter. placed constraints by on More monochromatic the mass recent dark functions. work matterrange has fraction of constituted possible revealed by primordial that primordial black using hole blackcome masses holes from (see lie diverse the across sources references a such in wide extra-galactic [ as gamma-ray microlensing emissions of from stars, black hole femtolensing evaporation of [ gamma-ray bursts, and ∼ ing chosen because the constraints are lesscase severe of than the anywhere else second in work theM [ parameter space. In the 10% of cosmological dark matterassumed in [ this mass range when monochromatic mass distributions are suggested as dark matter candidates [ which represent an alternate fate forof the matter death reaches of the a Planck blackinto density, roughly hole. a equivalent volumetric They to size form the near when concerned that[ a mass of collapsing being a shell compressed proton. Then, according to calculations , which is effectively a blackhorizon hole [ tunnelling into a whileof hole the and bouncing exploding black through hole its [ take event place on the order of a billion years for black holes larger than 10 via Hawking radiation [ due to the conjectured scale being Planckian [ electrons from falling onto an atomic nucleus [ to verification [ such an event we would require thethan presence a of solar primordial mass. black holes since they are much smaller [ Planck stars 1. Introduction gravity, perhaps at scales largerPlanck than stars the provide such Planckian an scale, avenue for would exploration. be Planck beneficial stars are to a modern recent phenomenon physics. [ larger than 10 PoS(HEASA2018)022 , i.e. (2.3) (2.1) (2.2) z will be is the as- χ ) z ( Justine Tarrant c BH R 2 5 in the LIGO window . 0 ∼ is the number density of ex- , ) pbh ) z f 2 L z ( , D ], allowing us to be as general as . N λ π ( 27 4 dz χ , but ) , ) z

. ]. This comparison allows one to set a z ( 26 τ ( M N dz . The above flux may also be used for the , d 28 c z BH 10 = τ 25 R d τ < dM 2 ) d ) ) z M ( M τ 2 ( is the spectral energy distribution of an individual ( N < N ) N z dz , dV = λ ) = ( z dz ( χ 0 dM eq , z 09 for 1 ) N . z Z 0 M ( is the differential co-moving volume element, ∼ N ) = λ dz dV ( pbh f Φ by noticing the following: ) z ( N is the co-moving distance at redshift L 05, ten times smaller than current timing arrays. Therefore the SKA will be . D ]. However, these constraints are strengthened with the implementation of the 2000 0 30 ∼ )[ pbh

f M In this paper we discuss the possible high-energy emission coming from Planck stars exploding This paper is organized as follows: section 2 gives a layout of the formalism used for calcu- The flux for the high-frequency background radiation generated by exploding Planck stars, Finally, we note that pulsar timing arrays also place constraints on the abundance of dark We may calculate 30 ∼ ( which is built up assumed follows: time taken for thethe emission time of taken to energy travel fromploding across the planck the stars primordial diameter at black of each hole redshift the exploding black at hole, where an invaluable resource to constrain the population in thesince future. the epoch of matter-radiation equality.evade We and consider satisfy lognormal constraints, mass as distributions mentioned which already.(see both Furthermore, figure we 1) compare the to spectra the obtained isotropic gamma-ray background [ lating the high-energy spectrum of thepresents Planck the stars data exploding used up for until comparison the within present spectra. section epoch. In 5. Section section 4 3 we discuss the results and conclude 2. High-energy emission from the time of matter-radiation equality till the present epoch, is given by making up theplaces Square Kilometre Array. In the same amount of observation time, SKA limit on the amount of energyalso going compare into the gamma-rays results as herein athat to a result earlier stringent of work constraint the is on placed Planck the on starmaking the low-energy amount explosion. emission. the of We energy Planck In released star both in either mechanism cases radio-bursts, we look or as gamma-rays, find less speculated to likely in to the account literature. for fast radio bursts or gamma-ray explosion and matter in the formyear of observation time primordial yields black holes. Using 143 known millisecond pulsars and a 30 Planck stars perturbations by a number ofpossible. inflationary scenarios [ accompanying low-energy signal, however thedifferent. form of the spectral energy distribution PoS(HEASA2018)022 ∼ pbh f (2.5) (2.4) pbh f , given are the Λ obs λ Ω Justine Tarrant and ]. Furthermore, . The latter will m 27 pbh , shifts around in the are the Planck time f Ω 0 using the temperature 26 pl χ , . χ M 4 has a thermal shape nor- 25 / 1 χ and ]. The first approach contains !# 5 pl 2 t / 3 ] − ) 2 1 . Here + ]. We then compare this data to the pre- z M ( 28 pl Λ m that allows the Planck star spectrum to ex- t ]. The lognormal distribution is convenient 2 0 Ω Ω 15 follows a thermal distribution. This is because χ  confidence level or more will be excluded. This , r χ pl pbh

σ 3 M 14 f , and has the single parameter M 1 to its mass −  obs of the total dark matter density being composed of τ λ = sinh τ pbh " f ) z + . Secondly, we may choose to normalise 1 0 ( χ em is the number density of Planck stars per unit mass. In this case we λ of the total mass-energy of the black hole and peaked at ) and 0 ∼ M χ ( pbh N f obs λ to some fraction are the observed and emitted wavelengths, respectively. ) , which is also peaked at is found through the following relationship [ , whilst the former option will allow for more freedom as em M ) ( λ τ d pbh obs N dM to be lognormal, following both [ f λ ) B and k M ( ( / obs ) N λ . Furthermore, any value of the product 0 hc ] Figure 1 shows the spectra for exploding Planck stars originating from primordial black holes The shape of the spectral energy distribution The term Our gamma-ray background data is sourced from [ ( χ 9 ∝ matter and cosmological constant density parameters, respectively [ under the assumption that primordial black holes may constitute the majority of dark matter ( where dicted high-energy background emission causedstar by emissions Planck over star all explosions. epochs We togrounds, expect contribute and the an here Planck extra we component to predictand the how isotropic large high-energy that back- component should be using the freeis parameters analogous to the treatment ofto the the low-energy extra-galactic signal background where light. we compared the predicted spectrum 4. Results ceed the isotropic gamma-ray background by a 3 as it fits a wide range of inflationary models for primordialprimordial black black holes. holes This [ is becausesince we know primordial how much black dark holes matter there areHere is weakly we in the interacting, treat universe Planck they and stars areassumption as means considered we being dark may made matter estimate of the candidates. number exploding of primordial Planck black stars holes, in the therefore universe. the last malised to some fraction the two free parameters the photon gas emitted upon explosionthe was spectral captured energy in the distribution hot in early two universe. ways. One may Firstly, normalise we assume that Planck stars which relates the lifetime of the black hole we normalise by [ T choose and mass, respectively. directly limit parameter space. 3. Isotropic gamma ray background PoS(HEASA2018)022

≤ M 0 χ 10 = , making µ pbh f , resulting in Justine Tarrant 39 − 10 1, we see that ≤ ∼ in which case the number pbh erg is released. Therefore, pbh f f 0 30 47 χ − 10 . For the case where 10 1. Considering the case where a ) ∼ erg is released, as we had above. . For ∼ ∼ M 38 ( 38 − N pbh pbh f f 10 ] we find 15 ≤ ) roughly and

9 5 [ pbh . − M f erg in energy. 0 7 0 10 − 38 χ 4 = ∼ 10 σ 0 ∼ χ and

erg when considering black hole we find that 10 M 9 9 fitting yields . Thus, very few Planck stars would result in gamma-ray bursts.

− 10 2 30 M 10 χ 7 − ≤ − = 10 µ ≤ parameter. When choosing to fix the normalisation according to the tem- pbh f 0 χ ]. Therefore, making it unlikely that Planck stars could result in fast radio ], a minimal 29 [ 14 34 − 25 [ . 10 0 erg energy release, thereby also placing a stringent constraint on the energy going into ≤ 8 = black hole would be present in the entire Milky Way, which is hard to reconcile with the and for a black hole exploding today ( erg. Similarly, for 9 10 For the low-energy signal we found that similar amounts of energy would be released, i.e. We also note that despite using two mass function models, i.e. Bellomo and Kuhnel, which Our results show some tension with the LIGO observations as they imply that less than one Probing quantum gravity is a non-trivial task. However, if objects like Planck stars exist, there Using the isotropic gamma-ray background, we were able to show that, for the models dis- The previous cases dealt with spectral energy distribution which was Planckian, where we Furthermore, suppose that instead a large portion of the energy from the Planck star explosion

σ 38 go into producing gamma-rays, i.e. take pbh f 10 M − ∼ 0 χ vary greatly in terms of their mean mass, only one order of separates their limits on Therefore to get ablack reasonable hole amount population producing of Planck energy stars, out, regardless of we the need spectral normalisation to used. severely reduce the primordial large amount of energy doesmordial go black into holes gamma-rays comes producing at Planckthe a stars events cost. is very rare. restricted Namely, the via population stringent of constraints pri- on bursts. 10 observed merger rate inferred byastrophysical LIGO. origin This rather tension than is primordial. releasedLIGO black if holes Therefore, all can’t LIGO if be black primordial. the holes Planck were star of hypothesis is true5. then Conclusion may be a window ontolow-energy component. quantum And gravity it is after suggestedbursts all. in whilst the the literature Two latter that main may the sigmals result formerchannel, in may are but gamma-ray result expected: note bursts. in that fast In a radio the thisthat high- article low-energy it and we signal is consider has unlikely the that a high-energy Planck similar stars fate: result in using fast the radio models burstscussed, herein or we gamma-ray we can bursts. show severely restrict thesion in total the energy present emitted epoch as to gamma-rays be from a Planck star explo- and of Planck stars producing gamma-raythey do bursts explode would they be will result very in small, a almost release of negligible. 10 But, when When we integrate over theing thermal from distribution an explosion to of extract a an 10 energy for the gamma-rays result- normalise using the perature, we find that did Planck stars 1). Both spectra are built using lognormal mass distributions 10 the amount of energy∼ going into gamma-rays duringa the explosion is stringentlygamma-rays. constrained These energies to are far too small to be considered as gamma-ray bursts. PoS(HEASA2018)022 ) Justine Tarrant ) 1 1 - 0 1 1105.6234 1401.6562 2 1 - PS Kuhnel PS Bellomo IGRB 0 Preprint ) 1 Classical and quantum gravity: , we find the results are the same. Preprint pbh f ) 012007 ( 3 1 and - 0 1442026 ( 0 erg. Furthermore, the Planck spectral energy 1 8 314 χ ] 1901.05827 m c D23 [ 5

λ vs 10 1010.3420 4 9 1 - 0 1 Preprint Preprint ( J. Phys. Conf. Ser. 5 1 - 0 Int. J. Mod. Phys. 1 6 1 - 0 2 3 4 0 1 9 - 1 1 1 1 1 1 - - - - - 0 0 0 0 0 0 ].

1

1 1 1 1 1

− − s m c . g r e E S E ] [ ) (

1 2 28 Comparison of high-frequency Planck star background (PS) to isotropic gamma ray background Theory, Analysis and Applications Therefore, the constraints obtained cast doubt upon whether or not the Planck stars described [2] Rovelli C and Vidotto F 2014 [3] Liberati S and Maccione L 2011 [4] Hossenfelder S 2010 Experimental Search for Quantum Gravity [1] Miao H, Martynov D and Yang H 2019 ( References Figure 1: (IGRB) data from [ Planck stars the Planck star high-energy emissions, i.e. 10 distribution and the thermal distribution normalizedother, using in the temperature that are under consistent the with each same circumstances for the using the models discussed hereature could since account either for a gamma-ray tiny bursts populationvery as rare), of speculated or primordial to one black in places holes stringent the is constraints liter- required the (making total their energy. occurrence Acknowledgements This work is based on the researchDepartment supported of by Science the and South Technology African and ResearchNo National Chairs 77948). Initiative Research of Foundation the of South Africa (Grant Therefore, the given insensitivityspectral to energy distributions changes suggests in that the the result mean is robust. mass and the consistency of the two PoS(HEASA2018)022 ) ) ) ) ) ) 0912.5297 Justine Tarrant ) Preprint 1204.2056 ) ) Preprint ) 1307.5798 astro-ph/0607207 Preprint ) 1409.4031 1607.06077 1501.07565 ) 036 1410.3696 104019 ( 229 Preprint Preprint (4) 584–587 URL 043001 ( 1404.5821 004 1611 Preprint 86 Preprint D81 158 ( 1701.07223 Preprint B807 01 D86 Preprint ) 1610.04234 123524 JCAP 786 86 ( 387–404 ( Preprint 1603.00464 127503 ( 083504 ( JCAP D87 023524 ( Preprint Phys. Rev. 799 469 D90 D94 Phys. Rev. Preprint Nucl. Phys. D92 Phys. Rev. Lett. Preprint 6 405–409 ( 1708.01789 Astrophys. J. 083508 ( Phys. Rev. 4244 023002 ( B739 199 Phys. Rev. D95 Phys. Rev. Astrophys. J. 201301 ( Phys. Rev. 43 D47 D95 Preprint 3756 2744 116 Astron. Astrophys. 30–31 478 415 75 0065 ( Phys. Lett. Phys. Rev. 1 A13 248 Phys. Rev. Phys. Rev. 152 594 MNRAS MNRAS a-Bellido J 2015 (Fermi-LAT) 2015 Nature Phys. Rev. Lett. A&A (EROS-2) 2007 MNRAS Comm. Math. Phys. Nat. Astron. et al. ) 2016 2016 et al. et al. et al. T J, Xu W, Taylor G B and Vermeulen R C 2001 https://link.aps.org/doi/10.1103/PhysRevLett.86.584 1902.02550 [5] Ade P [6] Rovelli C 2017 [7] Hawking S 1975 [8] Hawking S W 1974 [9] Barrau A, Rovelli C and Vidotto F 2014 [20] Wilkinson P N, Henstock D R, Browne I W A, Polatidis A G, Augusto P, Readhead A C S, Pearson [29] Tarrant J, Beck G and Colafrancesco S 2019 Probing quantum gravity at low energies ( [30] Schutz K and Liu A 2017 [21] Bird S [16] Carr B J, Kohri K, Sendouda Y and Yokoyama J 2010 [19] Tisserand P [22] Clesse S and Garcà [26] Dolgov A D, Kawasaki M and[27] Kevlishvili N 2009 Blinnikov S, Dolgov A, Porayko N[28] K andAckermann Postnov M K 2016 [25] Dolgov A and Silk J 1993 [17] Griest K, Cieplak A M and[18] Lehner MBarnacka J A, 2014 Glicenstein J F and Moderski R 2012 [24] Carr B and Silk J 2018 [13] Capela F, Pshirkov M and Tinyakov P[14] 2013 Bellomo N, Bernal J L, Raccanelli[15] A andKühnel Verde L F 2018 and Freese K 2017 [23] Carr B, Kuhnel F and Sandstad M 2016 [12] Hawkins M R S 2011 [11] Hawking S 1971 Planck stars [10] Barrau A and Rovelli C 2014