In the primordial universe, oscillations of heavy fields can be considered as standard clocks to measure the expansion or contraction history of the universe. Those standard clocks provide a model-independent way of distinguishing inflation and alternative scenarios. However, the mass of the heavy fields may not be a constant mass, but rather mass dynamically generated by non-minimal coupling to the Ricci scalar, or self-interactions. In the case of dynamically generated mass, the mass of the heavy field is generically of order Hubble, and thus is time-dependent in alternative to inflation scenarios. We show that such dynamically generated mass terms can be considered as non-standard primordial clocks for alternative to inflation, providing similar oscillatory frequencies as standard clocks of inflation. Additional information on scale dependence can distinguish such non-standard clocks from standard clocks.
We make an complementary investigation of the primordial trispectrum from exchanging intermediate scalar modes in multi-field inflation models with generalized kinetic terms. Together with the calculation of irreducible contributions to the primordial trispectrum in Ref.[103], we give the full leading-order primordial trispectrum in generalized multi-field models.
Standard Clocks in the primordial epoch leave a special type of features in the primordial perturbations, which can be used to directly measure the scale factor of the primordial universe as a function of time a(t), thus discriminating between inflation and alternatives. We have started to search for such signals in the Planck 2013 data using the key predictions of the Standard Clock. In this Letter, we summarize the key predictions of the Standard Clock and present an interesting candidate example in Planck 2013 data. Motivated by this candidate, we construct and compute full Standard Clock m…
We calculate the primordial trispectrum of curvature perturbation in quasi-single field inflation, with general sound speeds for both the inflaton and the massive scalar. Special attention is paid to various soft limits of the trispectrum, where the shape function shows characteristic oscillatory pattern (known as the quantum primordial standard clock signal) as a function of the momentum ratio. Our calculation is greatly simplified by using the "mixed propagator" developed under a diagrammatic representation of the in-in formalism.
Oscillating massive fields in the primordial universe can be used as Standard Clocks. The ticks of these oscillations induce features in the density perturbations, which directly record the time evolution of the scale factor of the primordial universe, thus if detected, provide a direct evidence for the inflation scenario or the alternatives. In this paper, we construct a full inflationary model of primordial Standard Clock and study its predictions on the density perturbations. This model provides a full realization of several key features proposed previously. We compare the theoretical predi…
In this paper, we point out and study a generic type of signals existing in the primordial universe models, which can be used to model-independently distinguish the inflation scenario from alternatives. These signals are generated by massive fields that function as standard clocks. The role of massive fields as standard clocks has been realized in previous works. Although the existence of such massive fields is generic, the previous realizations require sharp features to classically excite the oscillations of the massive clock fields. Here, we point out that the quantum fluctuations of massive…
We study primordial anisotropies generated in the model of gauged hybrid inflation in which the complex waterfall field is charged under a $U(1)$ gauge field. Primordial anisotropies are generated either actively during inflation or from inhomogeneities modulating the surface of end of inflation during waterfall transition. We present a consistent $δN$ mechanism to calculate the anisotropic power spectrum and bispectrum. We show that the primordial anisotropies generated at the surface of end of inflation do not depend on the number of e-folds and therefore do not produce dangerously large ani…
We revisit the idea of generating primordial anisotropies at the end of inflation in models of inflation with gauge fields. To be specific we consider the charged hybrid inflation model where the waterfall field is charged under a U(1) gauge field so the surface of end of inflation is controlled both by inflaton and the gauge fields. Using delta N formalism properly we find that the anisotropies generated at the end of inflation from the gauge field fluctuations are exponentially suppressed on cosmological scales. This is because the gauge field evolves exponentially during inflation while in …
We explain the motivation and main idea of our work in reference arXiv:0907.2476 [hep-th]. We present a simple model of multifield Dirac-Born-Infeld inflation whose bispectrum exhibits a linear combination of the equilateral and local shapes, which are usually considered as separate possibilities. We also point out the presence of a particularly interesting component of the primordial trispectrum.
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…
We set up cosmological perturbation theory and study the cosmological implications of the so-called ``generalized Galileon'' developed in \cite{Deffayet:2011gz,horndeski}. This is the most general scalar field theory whose Lagrangian contains derivatives up to second order while keeping second order equations of motion, and contains as sub-cases $k$-inflation, $G$-inflation and many other models. We calculate the power spectrum of the primordial curvature perturbation, finding a modification of the usual consistency relation of the tensor-to-scalar ratio in $k$-inflation or perfect fluid model…
We study the cosmological evolution of some nonlocal gravity models, when the initial conditions are set during a phase of primordial inflation. We examine in particular three models, the so-called RT, RR and $Δ_4$ models, previously introduced by our group. We find that the RR and $Δ_4$ models have a stable evolution also during inflation. The RT model has an apparent instability, but we show that, because of the smallness of the scale associated to the nonlocal term compared to the inflationary scale, this instability is innocuous and also the RT model has a viable evolution even when its in…
If long wavelength primordial tensor modes are coupled to short wavelength scalar modes, the scalar curvature two-point function will have an off-diagonal component. This `fossil' remnant is a signature of a mode coupling that cannot be achieved in single clock inflation. Any constraint on its presence allows a cross check of the relationship between the dynamical generation of the fluctuations and the evolution of the inflationary background. We use the example of non-Bunch Davies initial states for the tensor and scalar modes to demonstrate that physically reasonable fossils, consistent with…
Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparameterization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate concrete realizations of such a scenario, including non-minimal couplings between gravity and the fields driving inflation. We focus in particular on the dynamics of primordial gravitational waves and discuss how their properties depend on the pattern of symmetry breaking that we consider. Tensor modes can have a blue spectrum, and for the first time we build mod…
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 …
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.
The Universe is not just cold dark matter and dark energy, it also contains baryons, radiation and neutrinos. The presence of these components, beyond the pressure-less cold dark matter and the quasi-uniform dark energy ones, imply that the single clock assumption from inflation is no longer preserved. Here we quantify this effect and show that the single-clock symmetry is ensured only on scales where baryonic effects, neutrinos effects, or sound speed are zero. These scales depend on the cosmic epoch and the Universe composition. Hence for all use and purposes of interpreting state-of-the-art…
The large-scale power deficit in the cosmic microwave background fluctuations might be relevant with the physics of pre-inflation, a bounce, or a superinflationary phase preceding slow-roll inflation, which can provide a singular-free realization of inflation. We investigate the primordial perturbations from such pre-inflationary evolutions, which generally may consist of multiple phases with different background dynamics, and give a universal formula for the power spectrum of primordial perturbations in terms of the recursive Bogoliubov coefficients. We also apply our formula to corresponding…
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency range with assumption that the phase transition between two consecutive regimes to be abrupt during evolution of the Universe. The suppression of energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of energy spectrum of the primordial gravitational wav…
Massive fields in the primordial universe function as standard clocks and imprint clock signals in the density perturbations that directly record the scale factor of the primordial universe as a function of time, a(t). A measurement of such signals would identify the specific scenario of the primordial universe in a model-independent fashion. In this Letter, we introduce a new mechanism through which quantum fluctuations of massive fields function as standard clocks. The clock signals appear as scale-dependent oscillatory signals in the power spectrum of alternative scenarios to inflation.
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 generalize the consistency condition for the three-point function in single field inflation to the case of dissipative, multi-field, single-clock models. We use the recently introduced extension of the effective field theory of inflation that accounts for dissipative effects, to provide an explicit proof to leading (non-trivial) order in the generalized slow roll parameters and mixing with gravity scales. Our results illustrate the conditions necessary for the validity of the consistency relation in situations with many degrees of freedom relevant during inflation, namely that there is a pr…
We argue that primordial gravitational waves have a spectral break and its information is quite useful for exploring the early universe. Indeed, such a spectral break can be a fingerprint of the end of inflation, and the amplitude and the frequency at the break can tell us the energy scale of inflation and the reheating temperature simultaneously. In order to investigate the spectral break, we give an analytic formula for evolution of the Hubble parameter around the end of inflation where the slow roll approximation breaks down. We also evaluate the spectrum of primordial gravitational waves a…
In the primordial universe, fields with mass much larger than the mass-scale of the event-horizon (such as the Hubble parameter in inflation) exist ubiquitously, and can be excited from time to time and oscillate quickly around their minima. These excitations can induce specific patterns in density perturbations, which record the time dependence of the scale factor of the primordial universe, thus provide direct evidence for the inflation paradigm or its alternatives. Such effects are conventionally averaged out in theoretical and data analyses, but can be accessible for experiments targeting …
We study slow-roll inflation and the generation of primordial fluctuations in $F(T)$ gravity's rainbow. We obtain the second order action for scalar and tensor perturbations and then calculate the primordial power spectrum for them. Thus, after calculating the inflationary observables up to first order in slow-roll approximation, namely the scalar spectral index $n_{s}$ and the tensor-to scalar ratio $r$, we confront the predictions of the model with the current PLANCK and BICEP/Keck data.
Many cosmological models rely on large couplings of axions to gauge fields. Examples include theories of magnetogenesis, inflation on a steep potential, chiral gravitational waves, and chromonatural inflation. Such theories require a mismatch between the axion field range and the mass scale appearing in the $a F \widetilde{F}$ coupling. This mismatch suggests an underlying monodromy, with the axion winding around its fundamental period a large number of times. We investigate the extent to which this integer can be explained as a product of smaller integers in a UV completion: in the parlance o…
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 …
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.
This is a pedagogical review on primordial non-Gaussianities from inflation models. We introduce formalisms and techniques that are used to compute such quantities. We review different mechanisms which can generate observable large non-Gaussianities during inflation, and distinctive signatures they leave on the non-Gaussian profiles. They are potentially powerful probes to the dynamics of inflation. We also provide a non-technical and qualitative summary of the main results and underlying physics.
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 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.
The dS bubbles can nucleate spontaneously during inflation, and will be stretched by the cosmological expansion to astrophysical scale. We report on a novel phenomenon that such a bubble might develop into a gravastar (an ultra-compact object with a dS core) after inflation, which witnessed the occurrence of inflation and would survive till today. It is pointed out that if a primordial gravastar was involved in one of the LIGO/Virgo gravitational wave (GW) events, the post-merger object could be a gravastar that will eventually collapse into a black hole. As a result, the late-time GW ringdown…
Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in …
We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in criti…
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…
A model of inflation is presented where the inflaton field is a complex scalar field coupled to a U(1) gauge field. Due to the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by U(1). Due to the coupling of the inflaton to the gauge field, a time dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent U(1) gauge kinetic coupling.
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, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing flu…
The residuals of the power spectra of WMAP and Planck's cosmic microwave background (CMB) anisotropies data are known to exhibit a few interesting anomalies at different scales with marginal statistical significance. Combining bottom-up and top-down model-building approaches and using a pipeline that efficiently compares model predictions with data, we construct a model of primordial standard clock that is able to link and address the anomalies at both the large and small scales. This model, and its variant, provide some of the best fits to the feature anomalies in CMB. According to Bayes evid…
We describe extended theories which shares the gauge transformation symmetry of the T-models, and takes the T-models as well as Starobinsky model as special cases. We derive a general relation between the two slow-roll parameters, and find that a large class of models can be embedded. Such models include more general Starobinsky-like inflation as well as the chaotic inflation with a large tensor-to-scalar ratio consistent with the BICEP2 result.
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…
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 …
Inflation may provide unique insight into the physics at the highest available energy scales that cannot be replicated in any realistic terrestrial experiment. Features in the primordial power spectrum are generically predicted in a wide class of models of inflation and its alternatives, and are observationally one of the most overlooked channels for finding evidence for non-minimal inflationary models. Constraints from observations of the cosmic microwave background cover the widest range of feature frequencies, but the most sensitive constraints will come from future large-scale structure su…
We compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.
We show that current cosmic acceleration can be explained by an almost massless scalar field experiencing quantum fluctuations during primordial inflation. Provided its mass does not exceed the Hubble parameter today, this field has been frozen during the cosmological ages to start dominating the universe only recently. By using supernovae data, completed with baryonic acoustic oscillations from galaxy surveys and cosmic microwave background anisotropies, we infer the energy scale of primordial inflation to be around a few TeV, which implies a negligible tensor-to-scalar ratio of the primordia…
We show that if the propagating speed of gravitational waves (GWs) gradually diminishes during inflation, the power spectrum of primordial GWs will be strongly blue, while that of the primordial scalar perturbation may be unaffected. We also illustrate that such a scenario is actually a disformal dual to the superinflation, but it does not have the ghost instability. The blue tilt obtained is $0<n_T\lesssim 1$, which may significantly boost the stochastic GWs background at the frequency band of Advanced LIGO/Virgo, as well as the space-based detectors.
Inflationary scenarios in string theory often involve a large number of light scalar fields, whose presence can enrich the post-inflationary evolution of primordial fluctuations generated during the inflationary epoch. We provide a simple example of such post-inflationary processing within an explicit string-inflationary construction, using a Kahler modulus as the inflaton within the framework of LARGE Volume Type-IIB string flux compactifications. We argue that inflationary models within this broad category often have a selection of scalars that are light enough to be cosmologically relevant,…
Primordial blackholes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial blackholes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial blackholes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism fo…
We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.
Primordial null energy condition (NEC) violation would imprint a blue-tilted spectrum on gravitational wave background (GWB). However, its implications on the GWB might be far richer than expected. We present a scenario, in which after a slow-roll (NEC-preserving) inflation with Hubble parameter $H\simeq H_{inf1}$, the Universe goes through an NEC-violating period and then enters subsequent slow-roll inflation with a higher $H$ ($=H_{inf2}\gg H_{inf1}$). The resulting primordial gravitational wave spectrum is nearly flat at the cosmic microwave background band, as well as at the frequency $f\s…
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…
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.
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…
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…
