We show that, whenever the perturbations of some field are excited during inflation by a physical process on sub-horizon scales, they unavoidably generate, even through gravitational interactions alone, a significant resonant IR cascade of power down to scales that are of the order of the horizon at that time (we denote these scales as near IR). We provide general analytic one-loop results for the enhancement of the IR power of the curvature perturbation generated by this effect, highlighting the role played by the resonance. We then study a number of examples in which the excited state is: (i) an isocurvature field, (ii) the curvature perturbation itself, (iii) a mixture of curvature and isocurvature fluctuations driven to an excited state by their coupled dynamics. In the cases shown, the cascade significantly modifies the near IR part of the power spectrum of the curvature perturbation with respect to the linear theory, indicating that this effect can impact the phenomenology associated with a variety of mechanisms considered in the literature, notably concerning primordial black holes and gravitational waves.

We propose a new model-independent mechanism for producing primordial black holes from a period of multi-field inflation. This requires an enhancement of primordial fluctuations at short scales compared to their value at CMB scales. We show that such an amplification naturally occurs when the inflationary trajectory exhibits a strong turn, that is a limited period during which the trajectory strongly deviates from a geodesic in field space, and is sufficient for subsequently producing primordial black holes with the abundance to be all or a fraction of dark matter. Our mechanism is generic to models of inflation realized in a multi-dimensional field space with an overlying potential and geometry, also referred to as the inflationary landscape, as arises in embeddings of inflation in high-energy theories. We study analytically and numerically how the duration and the strength of the turn impact the primordial fluctuation power spectrum and the abundance of primordial black holes. Our mechanism has the potential of exhibiting unique features accessible to observation through the primordial black hole spectrum and the stochastic background of gravitational waves, offering a precious glimpse at the dynamics of inflation.

Oscillations in the frequency profile of the scalar-induced contribution to the stochastic gravitational wave background are a characteristic signal for small-scale features during inflation. We investigate how this oscillatory frequency profile is affected by the expansion history of the post-inflationary universe. Our results are applicable as long as the equation of state of the universe can be taken as constant during the period in which the gravitational waves are produced, and we compute the spectrum of gravitational waves induced by both sharp and resonant features, associated with oscillations in k and log(k), respectively. For resonant features, the frequencies of the oscillatory contributions to the gravitational wave spectrum are unaffected by the equation of state, but not their relative amplitudes, allowing one to extract information about both inflationary physics and the post-inflationary expansion history from the oscillatory pattern. For sharp features we find that the gravitational wave spectrum only exhibits prominent modulations as long as the propagation speed of density fluctuations is c(s) < 1, with a frequency larger by a factor c(s)(-1) than that of the scalar power spectrum. We find that the stiffer the equation of state, the larger the relative amplitude of the oscillations. In particular, a relative amplitude significantly higher than 20% is not achievable for the 'standard' case of radiation domination, and would be a smoking-gun signal of both nontrivial inflationary dynamics on small scales, and a post-inflationary universe not dominated by radiation.

SIGWfast is a python code to compute the scalar-induced gravitational wave spectrum from a primordial scalar power spectrum that can be given in analytical or numerical form. SIGWfast was written with the aim of being easy to install and use, and to produce results fast, typically in a matter of a few seconds. To this end the code employs vectorization techniques within python, but there is also the option to compile a C++ module to perform the relevant integrations, further accelerating the computation. The python-only version should run on all platforms that support python 3. The version employing the C++ module is only available for Linux and MacOS systems.

We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified with a strong turn in the inflationary trajectory. En passant, we derive a universal expression for the tensor power spectrum sourced at second order by an arbitrary number of scalar degrees of freedom during inflation, crucially taking into account the nontrivial structure of the Hilbert space in multifield setups. The SGWB sourced during inflation can overcome the standard scalar-induced SGWB sourced at horizon re-entry of the fluctuations after inflation, while being less constrained by perturbativity and backreaction bounds. In addition, one may entertain the possibility of detecting both since they peak at different frequencies exhibiting oscillations with distinct periods.

Oscillations in the frequency profile of the stochastic gravitational wave background are a characteristic prediction of small-scale features during inflation. In this paper we present a first investigation of the detection prospects of such oscillations with the upcoming space-based gravitational wave observatory LISA. As a proof of principle, we show for a selection of feature signals that the oscillations can be reconstructed with LISA, employing a method based on principal component analysis. We then perform a Fisher forecast for the parameters describing the oscillatory signal. For a sharp feature we distinguish between the contributions to the stochastic gravitational wave background induced during inflation and in the post-inflationary period, which peak at different frequencies. We find that for the latter case the amplitude of the oscillation is expected to be measurable with < 10% accuracy if the corresponding peak satisfies h 2ΩGW ≳ 10-12-10-11, while for inflationary-era gravitational waves a detection of the oscillations requires a higher peak amplitude of h 2ΩGW, as the oscillations only appear on the UV tail of the spectrum. For a resonant feature the detection prospects with LISA are maximised if the frequency of the oscillation falls into the range ω log = 4 to 10. Our results confirm that oscillations in the frequency profile of the stochastic gravitational wave background are a worthwhile target for future detection efforts and offer a key for experimentally testing inflation at small scales.

Cosmic inflation provides a window to the highest energy densities accessible in nature, far beyond those achievable in any realistic terrestrial experiment. Theoretical insights into the inflationary era and its observational probes may therefore shed unique light on the physical laws underlying our universe. This white paper describes our current theoretical understanding of the inflationary era, with a focus on the statistical properties of primordial fluctuations. In particular, we survey observational targets for three important signatures of inflation: primordial gravitational waves, primordial non-Gaussianity and primordial features. With the requisite advancements in analysis techniques, the tremendous increase in the raw sensitivities of upcoming and planned surveys will translate to leaps in our understanding of the inflationary paradigm and could open new frontiers for cosmology and particle physics. The combination of future theoretical and observational developments therefore offer the potential for a dramatic discovery about the nature of cosmic acceleration in the very early universe and physics on the smallest scales.

Abstract Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3.

We identify a characteristic pattern in the scalar-induced stochastic gravitational wave background from particle production during inflation. If particle production is sufficiently efficient, the scalar power spectrum exhibits 𝒪(1) oscillations periodic in k, characteristic of a sharp feature, with an exponentially enhanced envelope. We systematically study the properties of the induced spectrum of gravitational waves sourced after inflation and find that this inherits the periodic structure in k, resulting in a peak in the gravitational wave energy density spectrum with 𝒪(10 %) modulations. The frequency of the oscillation in the scalar power spectrum is determined by the scale of the feature during inflation and in turn sets the frequency of modulations in the gravitational wave signal. We present an explicit realisation of this phenomenon in the framework of multifield inflation, in the form of a strong sharp turn in the inflationary trajectory. The resulting stochastic background is potentially detectable in future gravitational wave observatories, and considerations of backreaction and perturbativity can be used to constrain the parameter space from the theoretical side. Our work motivates more extensive research linking primordial features to observable properties of the stochastic background of gravitational waves, and dedicated development in data analysis for their detection.

We propose a brane‐world setup based on gauge/gravity duality that permits the simultaneous realisation of self‐tuning of the cosmological constant and a stabilisation of the electroweak hierarchy. The Standard Model dynamics including the Higgs sector is confined to a flat 4‐dimensional brane, embedded in a 5‐dimensional bulk whose dynamics is governed by Einstein‐dilaton‐axion gravity. The inclusion of a dynamical bulk axion is new compared to previous implementations of the self‐tuning mechanism. Because of the presence of the axion, the model generically exhibits a multitude of static solutions, with different values for the equilibrium position for the brane. Under mild assumptions regarding the dependence of brane parameters on bulk fields, a number of these solutions exhibit electroweak symmetry breaking with a small Higgs mass as compared to the cutoff‐scale of the brane theory. The realisation of self‐tuning of the cosmological constant is generic and as efficient as in previous constructions without a bulk axion. Vacua with a small Higgs mass can sometimes be found, regardless of whether the brane theory depends explicitly on the bulk axion. Because it is expected on general principles that the brane action will depend on the axion, the generation of solutions with a hierarchy is a robust feature.

We analyse the post-inflationary contribution to the stochastic gravitational wave background due to a resonant feature in the scalar power spectrum, which is characterised by an oscillation in log(k), complementing our previous work arXiv:2012.02761 on sharp features. Primordial features signal departures of inflation from the single-field slow-roll paradigm and are motivated by embeddings of inflation in high energy physics. We find that the oscillation in the scalar power spectrum leads to a corresponding modulation in the gravitational wave spectrum that can be understood as a superposition of two oscillatory pieces, one with the original frequency of the scalar oscillations, and one with double frequency. For oscillations with slowly-varying amplitude this oscillatory part can be computed semi-analytically. Our results can be used as templates for the reconstruction of the signal from future data and permit extracting information about the small scale scalar power spectrum from measurements of the stochastic gravitational wave background.

We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-N quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant λ, there generically exist two backreacted constant-curvature solutions, as long as λ < λmax ∼ Mp2 / N2, otherwise no such solutions exist. Moreover, the backreaction effect interpolates between that of the UV and IR CFTs. We also find that, at finite cutoff, a holographic theory always reduces the bare cosmological constant, and this is the consequence of thermodynamic properties of the partition function of holographic QFTs on de Sitter.

We study F-functions in the context of field theories on S3 using gauge-gravity duality, with the radius of S3 playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. If the operator perturbing the UV CFT has dimension Δ > 3/2 these F -functions correspond to an appropriately renormalized free energy. If instead the perturbing operator has dimension Δ < 3/2 it is the quantum effective potential, i.e. the Legendre transform of the free energy, which gives rise to good F-functions. We check that these observations hold beyond holography for the case of a free fermion on S3 (Δ = 2) and the free boson on S3 (Δ = 1), resolving a long-standing problem regarding the non-monotonicity of the free energy for the free massive scalar. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.

Axionic holographic RG flow solutions are studied in the context of general Einstein-axion-dilaton theories. A non-trivial axion profile is dual to the (non-perturbative) running of the -term for the corresponding instanton density operator. It is shown that a non-trivial axion solution is incompatible with a non-trivial (holographic) IR conformal fixed point. Imposing a suitable axion regularity condition allows to select the IR geometry in a unique way. The solutions are found analytically in the asymptotic UV and IR regimes, and it is shown that in those regimes the axion backreaction is always negligible. The axion backreaction may become important in the intermediate region of the bulk. To make contact with the axion probe limit solutions, a systematic expansion of the solution is developed. Several concrete examples are worked out numerically. It is shown that the regularity condition always implies a finite allowed range for the axion source parameter in the UV. This translates into the existence of a finite (but large) number of saddle-points in the large Nc limit. This ties in well with axion-swampland conjectures.

Maximally symmetric curved-brane solutions are studied in dilatonic braneworld models which realise the self-tuning of the effective four-dimensional cosmological constant. It is found that no vacua in which the brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the near-boundary asymptotics of the bulk fields. In the holographic dual picture, this corresponds to coupling the UV CFT to a curved metric (possibly with a defect). Alternatively, the same may be achieved in a flat-space QFT with suitable variable scalar sources. With these ingredients, it is found that maximally symmetric, positive and negative curvature solutions with a stabilised brane position generically exist. The space of such solutions is studied in two different types of realisations of the self-tuning framework. In some regimes we observe a large hierarchy between the curvature on the brane and the boundary UV CFT curvature. This is a dynamical effect due to the self-stabilisation mechanism. This setup provides an alternative route to realising de Sitter space in string theory.

Holographic RG flows dual to QFTs on maximally symmetric curved manifolds (dSd, AdSd, and Sd) are considered in the framework of Einstein-dilaton gravity in d + 1 dimensions. A general dilaton potential is used and the flows are driven by a scalar relevant operator. The general properties of such flows are analyzed and the UV and IR asymptotics computed. New RG flows can appear at finite curvature which do not have a zero curvature counterpart. The so-called ‘bouncing’ flows, where the β-function has a branch cut at which it changes sign, are found to persist at finite curvature. Novel quantum first-order phase transitions are found, triggered by a variation in the d-dimensional curvature in theories allowing multiple ground states.

Protected by an approximate shift symmetry, axions are well motivated candidates for driving cosmic inflation. Their generic coupling to the Chern-Simons term of any gauge theory gives rise to a wide range of potentially observable signatures, including equilateral non-Gaussianites in the CMB, chiral gravitational waves in the range of direct gravitational wave detectors and primordial black holes (PBHs). In this paper we revisit these predictions for axion inflation models non-minimally coupled to gravity. Contrary to the case of minimally coupled models which typically predict scale-invariant mass distributions for the generated PBHs at small scales, we demonstrate how broadly peaked PBH spectra naturally arises in this setup. For specific parameter values, all of dark matter can be accounted for by PBHs.

The electric Weak Gravity Conjecture demands that axions with large decay constant f couple to light instantons. The resulting large instantonic corrections pose problems for natural inflation. We explore an alternative argument based on the magnetic Weak Gravity Conjecture for axions, which we try to make more precise. Roughly speaking, it demands that the minimally charged string coupled to the dual 2‐form‐field exists in the effective theory. Most naively, such large‐f strings curve space too much to exist as static solutions, thus ruling out large‐f axions. More conservatively, one might allow non‐static string solutions to play the role of the required charged objects. In this case, topological inflation would save the superplanckian axion. Furthermore, a large‐f axion may appear in the low‐energy effective theory based on two subplanckian axions in the UV. The resulting effective string is a composite object built from several elementary strings and domain walls. It may or may not satisfy the magnetic Weak Gravity Conjecture depending on how strictly the latter is interpreted and on the cosmological dynamics of this composite object, which remain to be fully understood. Finally, we recall that large‐field brane inflation is naively possible in the codimension‐one case. We show how string‐theoretic back‐reaction closes this apparent loophole of large‐f (non‐periodic) pseudo‐axions.

We present a particularly simple model of axion monodromy inflation: Our axion is the lowest-lying KK-mode of the RR-2-form-potential C2 in the standard Klebanov–Strassler throat. One can think of this inflaton candidate as being defined by the integral of C2 over the S2 cycle of the throat. It obtains an exponentially small mass from the IR-region in which the S2 shrinks to zero size. Crucially, the S2 cycle has to be shared between two throats, such that the second locus where the S2 shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. The inflaton back-reaction on the geometry turns out to be controlled by the string coupling gs. We hope that our setting is simple enough for many critical consistency issues of large-field inflation in string theory to be addressed at a quantitative level.