Abstract:We propose an alternative refined de Sitter conjecture. It is given by a natural condition on a combination of the first and second derivatives of the scalar potential. We derive our conjecture in the same weak coupling, semi‐classical regime where the previous refined de Sitter conjecture was derived, using the same tools together with a few more assumptions that we discuss. We further test and constrain free parameters in our conjecture using data points of a classical type IIA supergravity setup. Interestin… Show more
“…2 See [12] for the initial proposal, [13,14] for the potentially viable version, and [15,16] for further refinements. 3 By reliable, we mean that there are no unfixed moduli at positive vacuum energy, and therefore quantum corrections can be consistently ignored.…”
Demanding O(d, d)-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, b-field and dilaton, to all orders in α in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.
“…2 See [12] for the initial proposal, [13,14] for the potentially viable version, and [15,16] for further refinements. 3 By reliable, we mean that there are no unfixed moduli at positive vacuum energy, and therefore quantum corrections can be consistently ignored.…”
Demanding O(d, d)-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, b-field and dilaton, to all orders in α in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.
“…We also note that our study does not rely on the de Sitter swampland conjecture of Ref. [43] or its refinements [44][45][46][47][48][49][50]. Moreover, our arguments are not sensitive to the specific numerical coefficients in Eq.…”
mentioning
confidence: 78%
“…In particular, the SWGC as stated in Eq. (8) has been found [42] to be in phenomenological tension with the swampland de Sitter conjecture [43] as well as its refinements [44][45][46][47][48][49][50]. Some potential counterexamples involve axion-like particles and fifth-force constraints [51,52].…”
Scalar weak gravity conjectures (SWGCs) attempt to pinpoint the ranges of couplings consistent with a fundamental theory of all interactions. We identify a generic dynamical consequence of these conjectures for cosmology and show that SWGCs imply a particular behavior of the scalar fields in the early universe. A scalar field that develops a large expectation value during inflation must relax to the minimum of effective potential at a later time. SWGCs imply that a homogeneous distribution of the field is unstable with respect to fragmentation into localized lumps. This fragmentation can result in formation of stable solitons or primordial black holes, which can account for all or part of the dark matter, and also lead to generation of potentially observable gravitational waves.
“…For more recent discussions on the improvement and extension of this conjecture, see e.g. [20][21][22][23][24][25][26][27][28][29][30] and [31] for a review.…”
We study a model of two scalar fields with a hyperbolic field space and show that it reduces to a single-field Dirac-Born-Infeld (DBI) model in the limit where the field space becomes infinitely curved. We apply the de Sitter swampland conjecture to the two-field model and take the same limit. It is shown that in the limit, all quantities appearing in the swampland conjecture remain well-defined within the single-field DBI model. Based on a consistency argument, we then speculate that the condition derived in this way can be considered as the de Sitter swampland conjecture for a DBI scalar field by its own. The condition differs from those proposed in the literature and only the one in the present paper passes the consistency argument. As a byproduct, we also point out that one of the inequalities in the swampland conjecture for a multi-field model with linear kinetic terms should involve the lowest mass squared for scalar perturbations and that this quantity can be significantly different from the lowest eigenvalue of the Hessian of the potential in the local orthonormal frame if the field space is highly curved. Finally, we propose an extension of the de Sitter swampland conjecture to a more general scalar field with the Lagrangian of the form P (X, ϕ), where X = −(∂ϕ) 2 /2.
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