arXiv subjects

Andrei Linde

Publications and source records attributed to Andrei Linde.

At least 19 recordsLinked to original sources

arXiv2026

Quintessential \alpha-attractors, updated

Quintessential $\alpha$-attractor models of single-field inflation and evolving dark energy were constructed about a decade ago. Recently, it was pointed out that some of them might be disfavored due to dark-radiation constraints on gravitational waves and the higher values of $n_s$ favored by ACT. Here we present a class of updated quintessential $\alpha$-attractor models in which a single field describes both inflation and evolving dark energy, yields higher values of $n_s$, and admits reheating scenarios consistent with the dark-radiation bound on $\Delta N_{\rm eff}$. Depending on the value of the cosmological constant $\Lambda$, these models interpolate between $\Lambda$CDM with $\Lambda > 0$ (future dS universe), dynamical dark energy with $\Lambda = 0$ (future Minkowski universe), and dynamical dark energy with $\Lambda < 0$ (future cosmological collapse). We also study quintessential $\alpha$-attractor models based on an axion-inflaton complex scalar field with hyperbolic geometry, which describe inflation and dark energy of a ``phantom illusion'' type compatible with DESI DR2.

astro-ph.CO↗

arXiv2026

Waterfall-modulated $\alpha$-attractors

Hybrid $\alpha$-attractor models \cite{Kallosh:2022ggf} can have significantly greater values of $n_{s}$ and smaller $r$, while preserving the relation $r\cong 3\alpha (1-n_s)^2$, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field $\alpha$-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point $\varphi_c$. This allows one to increase the effective number of e-foldings $N_c$ in formulas like $n_s\simeq 1-{2\over N_c}$, $r\simeq {12 \alpha\over N_c^2}$. By changing the waterfall's steepness and location, one can continuously move the predictions along the curves with $r\cong 3\alpha (1-n_s)^2$ as $n_s$ increases and $r$ decreases. We also study the effect of waterfall insertions and uplift on $n_s$ in quintessential $\alpha$-attractors that describe inflation and dynamical dark energy.

astro-ph.CO↗

arXiv2026

Inflation, Open Universes, and Dark Energy

We study the impact of spatial curvature ($\Omega_k$) and dynamical dark energy (parametrized by $w_0$ and $w_a$) on the spectral index $n_s$ using a combination of cosmic microwave background datasets (Planck, SPT, and ACT), and spectroscopic galaxy samples from DESI, including both BAO and full-shape clustering measurements. We show that a small negative curvature, $\Omega_k\simeq 3\times 10^{-3}$, lowers the value of $n_s$, bringing it closer to predictions of the Starobinsky, Higgs, and simplest $\alpha$-attractor inflationary models. In particular, we find $n_s= 0.9667\pm0.0041$ (using Planck and DESI data) or $n_s= 0.9692\pm0.0035$ (adding ACT and SPT). Allowing for time-evolving dark energy also reduces the spectral index, leading to $n_s=0.9716\pm0.0032$ (from the combined dataset), or $n_s=0.9694\pm0.0035$ in combination with a small negative curvature. Our results demonstrate that the tension between current observational data and the Starobinsky, Higgs, and simplest $\alpha$-attractor models holds only for $\Lambda$CDM, and can be mitigated in extended cosmological models. We discuss implications of these findings for inflationary models in an open universe and/or with dynamical dark energy, including scenarios with quantum tunneling and non-standard topology. Furthermore, we briefly describe a special class of $\alpha$-attractor models, where one can make $n_s$ arbitrarily large, and we describe the $\alpha$-attractor quintessence model. Such models may be of particular relevance when future data from DESI, as well as DESI-II, SPHEREx, Euclid, Rubin, and Roman, becomes available.

astro-ph.CO↗

arXiv2026

Unification of polynomial and exponential cosmological attractors

We introduce a family of simple $\alpha$-attractor models that can interpolate between exponential and polynomial cosmological attractors. By varying the interpolation parameter $\mu$ in these models, one can scan a wide range of values of the spectral index $n_{s}$ matching any combination of CMB and DESI data.

hep-th↗

arXiv2026

New Exponential and Polynomial $\xi$-attractors

We introduce a new family of cosmological attractors with non-minimal coupling of gravity and non-canonical kinetic terms. In the Einstein frame, these models transform into a class of exponential and polynomial attractors with the spectral index $n_{s}$ spanning a broad range $1-2/N \leq n_{s} < 1-1/N$, and $r$ can decrease to zero in the limit $\xi \to \infty$. This is sufficient to match any combination of Planck, BICEP/Keck, ACT, SPT, and DESI data. We present a supergravity implementation of these models.

hep-th↗

arXiv2025

Singular $\alpha$-attractors

$\alpha$-attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of $\alpha$-attractors, T- and E-models, originate from theories with non-singular potentials. In canonical variables, these potentials have a plateau that is approached exponentially fast at large values of the inflaton field $\varphi$. In a closely related class of polynomial $\alpha$-attractors, or P-models, the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential also has a plateau, but it is approached polynomially. In this paper, we will consider a more general class of potentials, which can be singular at the boundary of the moduli space, S-models. These potentials may have a short plateau, after which the potential may grow polynomially or exponentially at large values of the inflaton field. We will show that this class of models may provide a simple solution to the initial conditions problem for $\alpha$-attractors and may account for a very broad range of possible values of $n_{s}$ matching the recent ACT, SPT, and DESI data.

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arXiv2025

Streamlined Supergravity

The textbook N=1 supergravity has an F-term potential depending on a superpotential $W(z_i)$ and a Kahler potential $K(z^i, \bar z^{\bar i})$, with the scalar potential $V(z^i, \bar z^{\bar i})=e^K (|DW|^2 - 3 |W|^2)$. In this approach, it is not always easy to find the potential $V(z^i, \bar z^{\bar i})$ with the required properties. We show that in supergravity with a nilpotent superfield and with any Kahler potential $K(z^i, \bar z^{\bar i} )$ one can obtain any desired potential $V(z^i, \bar z^{\bar i})$ by a proper choice of the Kahler metric of the nilpotent superfield. This construction is particularly suitable for cosmological and particle physics applications, which may require maximal freedom in the choice of kinetic terms and scalar potentials.

hep-th↗

arXiv2025

Alexei Starobinsky and Modern Cosmology

Alexei Starobinsky is one of the main authors of inflationary cosmology. Here I will discuss the Starobinsky model and its generalizations, including the theory of $\alpha$-attractors. I will then describe the current status of these models in light of the latest observational results from ACT, SPT, and DESI.

hep-th↗

arXiv2025

The BAO-CMB Tension and Implications for Inflation

The scalar spectral index $n_s$ is a powerful test of inflationary models. The tightest constraint on $n_s$ to date derives from the combination of cosmic microwave background (CMB) data with baryon acoustic oscillation (BAO) data. The resulting $n_s$ constraint is shifted significantly upward relative to the constraint from CMB alone, with the consequence that previously preferred inflationary models are seemingly disfavored by $\gtrsim 2 \sigma$. Here we show that this shift in $n_s$ is the combined effect of a degeneracy between $n_s$ and BAO parameters exhibited by CMB data and the tension between CMB datasets and DESI BAO data under the assumption of the standard cosmological model. Given the crucial role of $n_s$ in discriminating between inflationary models, we urge caution in interpreting CMB+BAO constraints on $n_s$ until the BAO-CMB tension is resolved.

astro-ph.CO↗

arXiv2025

Post-inflationary enhancement of adiabatic perturbations in modular cosmology

We show that multi-field inflationary models with negligible turning in field space during inflation can lead to an effective sourcing of adiabatic from entropic perturbations {\it after} the end of inflation. We illustrate this general phenomenon with a detailed analysis of an inflationary model whose scalar potential is determined by modular invariance. Its entropic perturbations are frozen during inflation, but instead, they are converted into adiabatic perturbations in the first post-inflationary $e$-folds. The curvature power spectrum, giving rise to CMB fluctuations, reaches a novel and enhanced plateau in this process; we address the implications for the inflationary observables $A_{s}$, $n_{s}$ and $r$.

astro-ph.CO↗

arXiv2025

On the Present Status of Inflationary Cosmology

We give a brief review of the basic principles of inflationary theory and discuss the present status of the simplest inflationary models that can describe Planck/BICEP/Keck observational data by choice of a single model parameter. In particular, we discuss the Starobinsky model, Higgs inflation, and $\alpha$-attractors, including the recently developed $\alpha$-attractor models with $SL(2,\mathbb{Z})$ invariant potentials. We also describe inflationary models providing a good fit to the recent ACT data, as well as the polynomial chaotic inflation models with three parameters, which can account for any values of the three main CMB-related inflationary parameters $A_{s}$, $n_{s}$ and $r$.

hep-th↗

arXiv2025

ACT, SPT, and chaotic inflation

We show that the simplest generalization of the chaotic inflation model $\tfrac12 {m^{2}\phi^{2}}$ with nonminimal coupling to gravity $(1+\phi) R$ provides a good match to the results of the latest data release of the Atacama Cosmology Telescope, with $r \approx10^{-2}$.

hep-th↗

arXiv2025

Axion Stabilization in Modular Cosmology

The $SL(2,\mathbb{Z})$ invariant $\alpha$-attractor models have plateau potentials with respect to the inflaton and axion fields. The potential in the axion direction is almost exactly flat during inflation, hence, the axion field remains nearly massless. In this paper, we develop a generalized class of such models, where the $SL(2,\mathbb{Z})$ symmetry is preserved, but the axion acquires a large mass and becomes strongly stabilized during inflation, which eliminates isocurvature perturbations in this scenario. Inflation in such two-field models occurs as in the single-field $\alpha$-attractors and leads to the same cosmological predictions.

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arXiv2025

Attractors in Supergravity

The concept of attractors, well-known in classical mechanics, proved to be very productive in supergravity, in the theory of black holes and inflationary cosmology. We start with attractors in supersymmetric black holes and discuss also non-BPS black hole attractors. Recently the non-BPS case helped to explain, via enhanced dualitiy symmetry, mysterious cancellation of ultraviolet divergences in 82 Feynman diagrams in 4-loop superamplitude in $N=5$ supergravity. We discuss the implications of these results for the possibility of the all-loop finiteness of $N > 4$ 4D supergravities. We continue with the description of inflationary $\alpha$-attractors. This large class of inflationary models gives predictions that are stable with respect to even very significant modifications of inflationary potentials. These predictions match all presently available CMB-related cosmological data. These models provide targets for the future satellite mission LiteBIRD, which will attempt to detect primordial gravitational waves. We describe some of the recent advanced versions of cosmological attractors which have a beautiful fractal landscape structure. Invited contribution to "Half a century of Supergravity", eds.~A. Ceresole and G.~Dall'Agata (Cambridge Univ. Press, to appear)

hep-th↗

arXiv2024

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

Recently proposed $SL(2,\mathbb{Z})$ invariant $\alpha$-attractor models have plateau potentials with respect to the inflaton and axion fields. The slope of the potential in the inflaton direction is exponentially suppressed at large values of the inflaton field, but the slope of the potential in the axion direction is double-exponentially suppressed. Therefore, the axion field remains nearly massless and practically does not change during inflation. The inflationary trajectory in such models is stable with respect to quantum fluctuations of the axion field. We show that isocurvature perturbations do not feed into the curvature perturbations during inflation, and discuss the possibility of such transfer at the post-inflationary stage.

hep-th↗

arXiv2024

Landscape of Modular Cosmology

We investigate the global structure of the recently discovered family of $SL(2,\mathbb{Z})$-invariant potentials describing inflationary $\alpha$-attractors. These potentials have an inflationary plateau consisting of the fundamental domain and its images fully covering the upper part of the Poincar\'e half-plane. Meanwhile, the lower part of the half-plane is covered by an infinitely large number of ridges, which, at first glance, are too sharp to support inflation. However, we show that this apparent sharpness is just an illusion created by hyperbolic geometry, and each of these ridges is physically equivalent to the inflationary plateau in the upper part of the Poincar\'e half-plane.

hep-th↗

arXiv2024

$SL(2,\mathbb{Z})$ Cosmological Attractors

We study cosmological theory where the kinetic term and potential have $SL(2,\mathbb{Z})$ symmetry. Potentials have a plateau at large values of the inflaton field, where the axion forms a flat direction. Due to the underlying hyperbolic geometry and special features of $SL(2,\mathbb{Z})$ potentials, the theory exhibits an $\alpha$-attractor behavior: its cosmological predictions are stable with respect to significant modifications of the $SL(2,\mathbb{Z})$ invariant potentials. We present a supersymmetric version of this theory in the framework of $\overline {D3}$ induced geometric inflation. The choice of $\alpha$ is determined by underlying string compactification. For example, in a CY compactification with $T^2$, one has $3\alpha=1$, the lowest discrete Poincar\'e disk target for LiteBIRD

hep-th↗

arXiv2022

Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds

We investigate the two-stage inflation regime in the theory of hybrid cosmological $\alpha$-attractors. The spectrum of inflationary perturbations is compatible with the latest Planck/BICEP/Keck results, thanks to the attractor properties of the model. However, at smaller scales, it may have a very high peak of controllable width and position, leading to a copious production of primordial black holes (PBH) and generation of a stochastic background of gravitational waves (SGWB).

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