[Paper Review] Cosmology at the top of the $\alpha'$ tower

Jerome Quintin, Heliudson Bernardo+1 more|arXiv (Cornell University)|May 3, 2021

Black Holes and Theoretical Physics169 references24 citations

TL;DR

This paper investigates cosmological solutions in string theory with all α′ corrections included via an O(d,d)-invariant action, focusing on matter coupling and singularity resolution. It shows that an infinite tower of α′ corrections enables fixed-dilaton de Sitter solutions even in vacuum and supports non-singular bouncing cosmologies in the Einstein frame, despite matter satisfying the null energy condition—offering a potential mechanism for resolving the big bang singularity within string cosmology.

ABSTRACT

The cosmology of the fully $\alpha'$-corrected duality-invariant action for the Neveu-Schwarz sector of string theory is revisited, with special emphasis on its coupling to matter sources. The role of the duality covariant pressure and dilatonic charge of the matter sector is explored in various contexts, from the low-curvature regime to non-perturbative solutions in $\alpha'$. We comment on how an infinite tower of $\alpha'$ corrections allows for fixed-dilaton de Sitter solutions, even in vacuum. We further investigate the necessary conditions for accelerated expansion in the Einstein frame, as well as for non-singular bounces that could resolve the big bang singularity. In particular, explicit examples are constructed, which show that the tower of $\alpha'$ corrections may support an Einstein-frame non-singular cosmological bouncing background, even when the matter sector respects the null energy condition.

Motivation & Objective

• To investigate the role of matter coupling in α′-complete, O(d,d)-invariant cosmological actions with all-order α′ corrections.
• To clarify the definition and physical role of pressure and dilatonic charge in duality-covariant cosmological models.
• To determine whether the infinite tower of α′ corrections can support non-singular bouncing cosmologies while respecting the null energy condition.
• To assess the viability of such models for resolving the big bang singularity in string cosmology.
• To examine the consistency of the theory with known limits, such as Einstein gravity and linear dilaton CFTs.

Proposed method

• Formulates the fully α′-corrected, O(d,d)-invariant action for the Neveu-Schwarz sector of string theory, including all higher-curvature corrections.
• Derives equations of motion for the metric, dilaton, and b-field under time-dependent, homogeneous, and isotropic assumptions.
• Introduces a duality-covariant definition of pressure and dilatonic charge to handle matter coupling in the O(d,d) framework.
• Applies a general Weyl transformation to map the string frame to the Einstein frame, enabling analysis of energy conditions and Hubble evolution.
• Constructs explicit ansätze for the Hubble rate H(t) in the string frame, including DBI-like and functional renormalization group-inspired forms.
• Evaluates energy conditions (SEC and NEC) in the Einstein frame to assess conditions for accelerated expansion and non-singular bounces.

Experimental results

Research questions

• RQ1 Can fixed-dilaton de Sitter solutions exist in vacuum within the α′-complete, O(d,d)-invariant cosmological action?
• RQ2 How does the duality-covariant pressure and dilatonic charge of matter influence cosmological evolution in the α′-tower regime?
• RQ3 Under what conditions can the infinite tower of α′ corrections lead to non-singular bouncing solutions in the Einstein frame?
• RQ4 Can non-singular bounces be achieved even when the matter sector satisfies the null energy condition?
• RQ5 What are the constraints on the equation of state of matter in the low- and high-curvature limits of the α′-corrected theory?

Key findings

• The infinite tower of α′ corrections allows for fixed-dilaton de Sitter solutions even in vacuum, demonstrating that such solutions are not restricted to matter-coupled scenarios.
• The duality-covariant pressure and dilatonic charge are essential for consistent matter coupling in the O(d,d)-invariant framework, and their definitions differ from standard ones in general relativity.
• Non-singular bouncing solutions can be supported in the Einstein frame by the α′-tower, even when the matter sector satisfies the null energy condition.
• Explicit toy models of bouncing cosmologies were constructed that remain non-singular throughout time, serving as a proof of principle for singularity resolution.
• The low- and high-curvature limits constrain the allowed equations of state of matter, with the high-energy limit favoring specific EoS consistent with the α′-corrected dynamics.
• While simple F(H) functions could not fully resolve singularities, the results suggest that more complex functional forms or additional structures—such as non-local dilaton potentials—may be necessary for complete singularity resolution.