Accelerating cosmology from $Λ<0$ gravitational effective field theory

TL;DR

This work investigates cosmologies from gravitational EFTs with $Λ<0$ and holographic duals, arguing that time-dependent scalar fields generically yield realistic FRW histories with a period of acceleration and with asymptotically AdS Euclidean continuations. It shows that acceleration can occur without fine-tuning in explicit EFT examples, and that suitably tuned potentials can reproduce $Λ$CDM to high accuracy, including a consistent wormhole (Euclidean) interpretation. The paper also demonstrates that the relevant scalar potentials can be derived from a superpotential in $\mathcal{N}=1$ supergravity, providing a concrete SUSY embedding pathway and a method to construct $W$ so that $V_W$ closely matches $V$. Taken together, these results point to a holographically flavored, supersymmetric EFT framework capable of generating realistic cosmological histories while retaining a clear connection to AdS/CFT structures, laying groundwork for future fluctuations analyses and microscopic constructions.

Abstract

A large class of $Λ< 0$ cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a $Λ$CDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

Figures (11)

• Figure 1: Evolution of the scalar field in a typical potential in the cosmology and its Euclidean continuation.
• Figure 2: Space of model parameter $g$ and initial condition $\phi_0$ for the exponential potential of (\ref{['eq:exppot']}) and (\ref{['eq:intpot']}). Solutions of the equations of motion (\ref{['eq:cosmoeom']}) and (\ref{['eq:wormeom']}) with parameter $g$ and initial condition $\phi_0$ contained in the red region exhibit an accelerating phase.
• Figure 3: Panel (A) is the same as Figure \ref{['fig:paramspace']} with $m^2=-9/4$. Panels (B), (C), and (D) correspond to masses $m^2=-8/4$, $m^2=-7/4$, and $m^2=-6/4$, respectively. Clearly it becomes much less generic to have a period of accelerated expansion as $m^2$ increases.
• Figure 4: An example of the potential (\ref{['eq:flatpot']}). $A$ fixes the value of $\tilde{V}>0$ at the plateau, $B$ the value of $\tilde{V}(0)$, i.e. the negative cosmological constant in the asymptotically AdS regions of the wormhole solution. $C$, $X$, $\Delta$ determine the depth, location, and width of the deep valleys present in the potential.
• Figure 5: Scale factor evolution for the cosmological solution obtained using the Planck cosmological parameters (\ref{['eq:planckdata']}) (denoted by "CVac"). The potential parameters are given in equation (\ref{['eq:numpotparam']}). The scale factor for the corresponding $\Lambda$CDM solution is also depicted. The two scale factors are indistinguishable until the present day $\tilde{t}=\tilde{t}_{0}=-1.16342$ (where $a(\tilde{t}_0)=1$) --- indicated by the black dashed line --- and beyond. Deviations in our solution from the $\Lambda$CDM behavior become evident at late times as the universe approaches the turning point at $\tilde{t}=0$. The contraction phase in our solution, not depicted here, can be obtained by time-reversal.