We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of Schwarzschild-de Sitter like metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instantaneously equal to the value of the scalar potential. The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the fractional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The "mass first law" and the "Schwarzschild-de Sitter patch first law" of thermodynamics are satisfied throughout the evolution.
We speculate that the early Universe was inside a primordial black hole. The interior of the the black hole is a dS background and the two spacetimes are separated on the surface of black hole's event horizon. We argue that this picture provides a natural realization of inflation without invoking the inflaton field. The black hole evaporation by Hawking radiation provides a natural mechanism for terminating inflation so reheating and the hot big bang cosmology starts from the evaporation of black hole to relativistic particles. The quantum gravitational fluctuations at the boundary of black ho…
We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the …
We propose an extension of the scalaron-Higgs model by a non-minimal coupling of the Standard Model Higgs boson to the quadratic Ricci scalar resulting in a Higgs-dependent scalaron mass. The model predicts a successful stage of effective single-field Starobinsky inflation. It features a multi-field amplification mechanism leading to a peak in the inflationary power spectrum at small wavelengths which enhances the production of primordial black holes. The extended scalaron-Higgs model unifies inflationary cosmology with elementary particle physics and explains the origin of cold dark matter in…
We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter $c_s$ during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, prov…
We introduce inflationary models where the inflaton features a field dependent non-minimal derivative coupling to the Einstein tensor, that we name GNMDC. This Horndeski term gives new and distinguishable inflationary predictions in a framework that ameliorates possible problems related with gradient instabilities during the reheating stage. We examine the inflationary phenomenology using power law monomial and exponential potentials. We further elaborate on the implications of the inflaton-modulated GNMDC and construct GNMDC terms that can amplify the power spectrum of primordial perturbation…
We study a possible amplification mechanism for the curvature perturbations generated during inflation by a Dirac-Born-Infeld (DBI) inflaton in the presence of a sharp feature in the warp factor. The large growth resulting in the scalar power spectrum is a consequence of the decreasing speed of sound. We obtain analytical approximate expressions for the relevant dynamical quantities both in the slow roll phase and during the transient phase which leads to the amplification. We finally compare our approximations to the exact numerical evolution and give, in such a context, the general rules for…
In this paper we study the survival of entanglement of a scalar field state created during inflation. We find that there exist UV-finite subdominant contributions to the entanglement entropy per momentum mode that scale with the number of e-folds between horizon exit and the end of inflation, and depend on the logarithm of the radius of the entangling surface, which can be taken to be the horizon sphere. We argue that this entanglement entropy allows for the formation of entangled Primordial Black Holes (PBH). We find that the entropy arising from the entanglement between PBH is small compared…
The next generation of space-borne gravitational wave detectors may detect gravitational waves from extreme mass-ratio inspirals with primordial black holes. To produce primordial black holes which contribute a non-negligible abundance of dark matter and are consistent with the observations, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a very flat potential for the inflaton, and this will increase the number of $e$-folds. To avoid the problem, an ultra-slow-roll inflation at the near inflection point …
In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
We propose a simple analytic fit for the power spectrum of scalar (curvature) perturbations during inflation, in order to describe slow roll of inflaton and formation of primordial black holes in the early universe, in the framework of single-field models. Our fit is given by a sum of the power spectrum in the slow-roll approximation, needed for a viable description of the cosmic microwave background radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient production of primordial black holes. W…
We propose and study the new (generalized) E-type $α$-attractor models of inflation, in order to include formation of primordial black holes (PBHs). The inflaton potential has a near-inflection point where slow-roll conditions are violated, thus leading to large scalar perturbations collapsing to PBHs later. An ultra-slow roll (short) phase exists between two (longer) phases of slow-roll inflation. We numerically investigate the phases of inflation, derive the power spectrum of scalar perturbations and calculate the PBHs masses. For certain values of the parameters, the asteroid-size PBHs can …
Dilatonic Charged Nariai instantons mediate the nucleation of black hole pairs during extended chaotic inflation. Depending on the dilaton and inflaton fields, the black holes are described by one of two approximations in the Lorentzian regime. For each case we find Euclidean solutions that satisfy the no boundary proposal. The complex initial values of the dilaton and inflaton are determined, and the pair creation rate is calculated from the Euclidean action. Similar to standard inflation, black holes are abundantly produced near the Planck boundary, but highly suppressed later on. An unusual…
I present a very simplistic toy model for the inflationary paradigm where the size of the universe undergoes a period of exponential growth. The basic assumption I make use of is that black holes might have a quantized area (mass) spectrum with a stable ground state and that the universe has started with a tightly packed collection of these objects alone.
Primordial black holes are produced in a minimal UV extension to the Higgs inflation with an included $R^2$ term. We show that for parameters consistent with Standard Model measurements and Planck observation results lead to $M_{\rm PBH} \in (10^{-16}, 10^{-15}) M_\odot$ primordial black holes with significant abundance, which may consist the majority of dark matter.
Primordial black holes (PBHs) can generically form in inflationary setups through the collapse of enhanced cosmological perturbations, providing us access to the early Universe through their associated observational signatures. In the current work we propose a new mechanism of PBH production within non-canonical inflation, using a class of steep-deformed inflationary potentials compatible with natural values for the non-canonical exponents. In particular, by requiring significant PBH production we extract constraints on the non-canonical exponents. Additionally, we find that our scenario can l…
It has been recently proposed that the interior of a black hole is vacuum energy, and this offers a possible explanation for the dark energy of the current observable universe. In this article we explore the idea that black holes are a source of vacuum energy in the early universe as well, and could possibly explain early inflation. Our scenario pre-supposes a single aboriginal black hole as the source of vacuum energy that drives inflation and eventually evaporates due to Hawking radiation. In such a model we can estimate $t_i $ and $t_f $ which are the times when inflation began and ended re…
This paper is a major revision of our previous work on the HST model of inflation. We identify the local fluctuations of the metric with fluctuations of the mass and angular momentum of black holes, and show that the consistency conditions in HST for a single trajectory to see more and more of a homogeneous distribution of black holes, imply that the system outside the horizon is undergoing inflation: small systems of equal entropy, are not in causal contact. Homogeneity then requires that the initial trajectory underwent inflation that expanded the black hole radius into our current horizon. …
Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe ina…
We revisit the model of axion inflation in the context of stochastic inflation and investigate the effects of the stochastic noises associated to the electromagnetic fields. Because of the parity violating interaction, one polarization of the gauge field is amplified inducing large curvature perturbation power spectrum. Taking into account the stochastic kicks arising from the short modes at the time of horizon crossing we obtain the corresponding Langevin equations for the long modes of the electromagnetic and axion fields. It is shown that a mean-reverting process governs the dynamics of the…
We study a model of two-field ultra-slow-roll (USR) inflation bounded by a curve in the field space. Curvature perturbations and non-Gaussianities can be enhanced both during the USR phase and from the inhomogeneities at the boundary. We employ the full non-linear $δN$ formalism to calculate the probability distribution function (PDF) for curvature perturbation non-perturbatively and show that the non-linear effects can significantly enhance the abundance of the primordial black holes (PBHs). For large curvature perturbations, the PDF has a universal exponential tail, but for the intermediate …
The most up to date femto- and micro-lensing constraints indicate that primordial black holes of $\sim 10^{-16} M_\odot$ and $\sim 10^{-12} M_\odot$, respectively, may constitute a large fraction of the dark matter. We describe analytically and numerically the dynamics by which inflationary fluctuations featuring a time-varying propagation speed or an effective Planck mass can lead to abundant primordial black hole production. As an example, we provide an ad hoc DBI-like model. A very large primordial spectrum originating from a small speed of sound typically leads to strong coupling within th…
We present a single-field string inflationary model which allows for the generation of primordial black holes in the low mass region where they can account for a significant fraction of the dark matter abundance. The potential is typical of type IIB fibre inflation models and features a plateau at CMB scales and a near inflection point at large distance scales where the power spectrum is enhanced due to a period of ultra slow-roll. The tunability of the underlying parameters is guaranteed by scanning through the string landscape and their stability against quantum corrections is ensured by an …
It is well known that a primordial black hole (PBH) can be generated in the inflation process of the early universe, especially when the inflation field has a number of non-trivial features that could break the slow-roll condition. In this study, we investigate a toy model of inflation with bumpy potential, which has one or several bumps. We determined that the potential with multi-bump can generate power spectra with multi-peaks in small-scale region, which can in turn predict the generation of primordial black holes in various mass ranges. We also consider the two possibilities of PBH format…
We extend the Cecotti-Kallosh model of Starobinsky inflation in supergravity by adding a holomorphic function to the superpotential in order to generate a large peak in the power spectrum of scalar (curvature) perturbations. In our approach, the singular non-canonical kinetic terms are largely responsible for inflation (as an attractor solution), whereas the superpotential is engineered to generate a production of primordial black holes. We study the cases with (i) a linear holomorphic function, (ii) a quadratic holomorphic function, and (iii) an exponential holomorphic function, as regards th…
In response to a recent criticism, appeared in arXiv:2303.00341, we argue that the standard scenario to form primordial black holes in the early universe based on a phase of ultra-slow-roll in single-field inflation is not ruled out.
We discuss a two-step mechanism to create a new inflationary domain beyond a wormhole throat which is created by a phase transition around an evaporating black hole. The first step is creation of a false vacuum bubble with a thin-wall boundary by the thermal effects of Hawking radiation. Then this wall induces a quantum tunneling to create a wormhole-like configuration. As the space beyond the wormhole throat can expand exponentially, being filled with false vacuum energy, this may be interpreted as creation of another inflationary universe in the final stage of the black hole evaporation.
Black holes of multiple horizons without mass inflation
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文学与空间科学学院）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Department of Physics, Kazakh National Women’s Teacher Training University（哈萨克斯坦国立女子师范大学物理系）
We construct an analytically solvable simplified model that captures the essential features for primordial black hole (PBH) production in most models of single-field inflation. The construction makes use of the Wands duality between the constant-roll (or slow-roll) and the preceding ultra-slow-roll phases and can be realized by a simple inflaton potential of two joined parabolas. Within this framework, it is possible to formulate explicit inflationary scenarios consistent with the CMB observations and copious production of PBHs of arbitrary mass. We quantify the variability of the shape of the…
We derive two new equations of quantum gravity and combine them with reinterpretations of previously proposed concepts of dark energy, black holes, inflation, the arrow of time and the energy at which rest-mass first manifests itself into a theory which may be a first step toward a comprehensive description of all these phenomena. The resulting theory also predicts new tests which can be experimentally checked within a few years.
It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the Cosmic Microwave Background (CMB) exceeds 10^(-4). This value is within the bounds allowed by astrophysical phenomena for the small scale spectrum of the CMB, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et. al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show…
We study a mechanism for the amplification of the inflationary scalar perturbation when the inflaton field action is non-canonical, i.e. the inflaton kinetic term has a non-standard form. For such a case the speed of sound of the perturbations generated during inflation is less than one and in general changes with time. Furthermore in such models, even when the scalar field potential is negligible, diverse inflationary attractors may exist. The possible effects of a speed of sound approaching zero during some stage of inflation may lead to a large amplification for the amplitude of the scalar …
Inspired from the inflation brane world cosmology, we study the thermodynamics of a black hole solution in two dimensional dilaton gravity with an arctangent potential background. We first derive the two dimensional black hole geometry, then we examine its asymptotic behaviors. More precisely, we find that such behaviors exhibit properties appearing in some known cases including the Anti de Sitter and the Schwarzchild black holes. Using the complex path method, we compute the Hawking radiation. The entropy function can be related to the value of the potential at the horizon.
We present a novel mechanism for the production of primordial black holes (PBHs). The mechanism is based on a period of thermal inflation followed by fast-roll inflation due to tachyonic mass of order the Hubble scale. Large perturbations are generated at the end of the thermal inflation as the thermal inflaton potential turns from convex to concave. These perturbations can lead to copious production of PBHs when the relevant scales re-enter horizon. We show that such PBHs can naturally account for the observed dark matter in the Universe when the mass of the thermal inflaton is about $10^6\,$…
We summarise recent work on the quantum production of black holes in the inflationary era. We describe, in simple terms, the Euclidean approach used, and the results obtained both for the pair creation rate and for the evolution of the black holes.
We analytically derive a class of non-singular, static and spherically symmetric topological black hole metrics inF(R)-gravity. These have not a de Sitter core at their centre, as most model in standard General Relativity. We study the geometric properties and the motion of test particles around these objects. Since they have two horizons, the inner being of Cauchy type, we focus on the problem of mass inflation and show that it occurs except when some extremal conditions are met.
We propose a new potential in brane inflation theory, which is given by the arctangent of the square of the scalar field. Then we perform an explicit computation for inflationary quantities. This potential has many nice features. In the small field approximation, it reproduces the chaotic and MSSM potentials. It allows one, in the large field approximation, to implement the attractor mechanism for bulk black holes where the geometry on the brane is de Sitter. In particular, we show, up to some assumptions, that the Friedman equation can be reinterpreted as a Schwarzschild black hole attractor …
In the axion monodromy inflation, the inflation is driven by the axion with super-Planckian field values in a monomial potential with superimposed sinusoidal modulations. The coupling of the axion to massless gauge fields can induce copious particle production during inflation, resulting in large non-Gaussian curvature perturbation that leads to the formation of primordial black holes. In this paper, we explore the parameter space in the axion monodromy inflation model that favors the formation of primordial black holes with masses ranging from $10^8$ grams to $20$ solar masses. We also study …
We consider the possibility that the majority of dark matter in our Universe consists of black holes of primordial origin. We determine the conditions under which such black holes may have originated from a single-field model of inflation characterized by a quartic polynomial potential. We also explore the effect of higher-dimensional operators. The large power spectrum of curvature perturbations that is needed for a large black hole abundance sources sizable second order tensor perturbations. The resulting stochastic background of primordial gravitational waves could be detected by the future…
We study the effect of supergravity corrections due to a linear and a bilinear term in the Kähler potential, in the context of a supersymmetric hybrid inflation model. By appropriate choice of the parameters associated to these terms, we are able to satisfy the main cosmological constraints for the spectral index $n_s$ and the tensor-to-scalar ratio $r$. In addition, this model predicts primordial black hole abundance enough to account for the whole dark matter of the Universe and gravitational wave spectra within the reach of future detection experiments. The predictions of the model can be m…
We study the generation of a large power spectrum, necessary for primordial black hole formation, within the effective theory of single-field inflation. The mechanisms we consider include a transition into a ghost-inflation-like phase and scenarios where an exponentially growing mode is temporarily turned on. In the cases we discuss, the enhancement in the power spectrum results from either a swift change in some effective coupling or a modification of the dispersion relation for the perturbations, while the background evolution remains unchanged and approximately de Sitter throughout inflatio…
We analyze the interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory. Generically the solutions exhibit a behaviour that may be described as ``mass inflation'', although with a remarkable difference between the cases with and without a Higgs field. Without Higgs field the YM field induces a kind of cyclic behaviour leading to repeated cycles of mass inflation - taking the form of violent explosions - interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur. In addition ther…
We study the phenomena of mass inflation using the Ori model for a rotating BTZ black hole that is sufficiently far from extremality, and show that the right Cauchy horizon ($\mathcal{CH}^+_R$) of the BTZ black hole becomes singular. Motivated by the recent analysis of Dias, Reall, Santos [J. High Energy Phys. 12 (2019) 097], we choose the retrograde quasinormal modes to govern the decay of perturbations exterior to the black hole. The resulting model captures the violation of the strong cosmic censorship conjecture near extremality. On the other hand, far from extremality, the $\mathcal{CH}^+…
We study the inner dynamics of accreting Eddington-inspired Born-Infeld black holes using the homogeneous approximation and taking charge as a surrogate for angular momentum. We show that there is a minimum of the accretion rate below which mass inflation does not occur, and we derive an analytical expression for this threshold as a function of the fundamental scale of the theory, the accretion rate, the mass, and the charge of the black hole. Our result explicitly demonstrates that, no matter how close Eddington-inspired Born-Infeld gravity is to general relativity, there is always a minimum …
We study the prospects of detection at terrestrial and space interferometers, as well as at pulsar timing array experiments, of a stochastic gravitational wave background which can be produced in models of axion inflation. This potential signal, and the development of these experiments, open a new window on inflation on scales much smaller than those currently probed with Cosmic Microwave Background and Large Scale Structure measurements. The sourced signal generated in axion inflation is an ideal candidate for such searches, since it naturally grows at small scales, and it has specific proper…
We adapted the Appleby-Battye-Starobinsky model of $F(R)$ gravity towards describing double cosmological inflation and formation of primordial black holes with masses up to $10^{19}$ g in the single-field model. We found that it is possible to get an enhancement of the power spectrum of scalar curvature perturbations to the level beyond the Hawking (black hole evaporation) limit of $10^{15}$ g, so that the primordial black holes resulting from gravitational collapse of those large primordial perturbations can survive in the present universe and form part of cold dark matter. Our results agree …
A standard scenario to form primordial black holes in the early universe is based on a phase of ultra-slow-roll in single-field inflation when the amplitude of the short scale modes is enhanced compared to the CMB plateau. Based on general arguments, we show that the loop corrections to the large-scale linear power spectrum from the short modes are small and conclude that the scenario is not ruled out.
We summarize our work on the generation of primordial black holes in a type of two-field inflationary models. The key ingredient is a sharp turn of the background trajectory in field space. We show that certain classes of solutions to the equations of motion exhibit precisely this kind of behavior. Among them we find solutions, which describe a transition between an ultra-slow roll and a slow roll phases of inflation.
We consider the impact of quantum diffusion on inflationary dynamics during an ultra-slow-roll phase, which can be of particular significance for the formation of primordial black holes. We show, by means of a fully analytical approach, that the power spectrum of comoving curvature perturbations computed in stochastic inflation matches precisely, at the linear level, the result obtained by solving the Mukhanov-Sasaki equation, even in the presence of an ultra-slow-roll phase. We confirm this result numerically in a model in which the inflaton has a polynomial potential and is coupled quadratic…
