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Register a new userThe four-dimensional null energy condition as a swampland conjecture
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Added by
Suddhasattwa Brahma
Publication date
2021
fields
Physics
and research's language is
English
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We analyze four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmologies in type IIB, arising from a M-theory dual, and find that the null energy condition (NEC) has to be obeyed by them (except for the negatively curved case) in order for the M-theory action to have a Wilsonian effective description. However, this does not imply that the M-theory metric has to obey the 11d NEC. Thus, we propose a new swampland conjecture -- the 4d NEC is a consistency condition for any theory to have a completion within M-theory -- with an explicit derivation of it for cosmological backgrounds from a top-down perspective. We briefly discuss the cosmological consequences of such a condition derived from M-theory.
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We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking $dot H>0$ in scalar tensor theories of gravity.
We argue that, in the presence of time-dependent fluxes and quantum corrections, four-dimensional de Sitter solutions should appear in the type IIB string landscape and not in the swampland. Our construction considers generic choices of local and non-local quantum terms and satisfies the no-go and the swampland criteria, the latter being recently upgraded using the trans-Planckian cosmic censorship. Interestingly, both time-independent Newton constant and moduli stabilization may be achieved in such backgrounds even in the presence of time-dependent fluxes and internal spaces. However, once the time-dependence is switched off, any four-dimensional solution with de Sitter isometries appears to have no simple effective field theory descriptions and is back in the swampland.
We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the Stuckelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further evidence for the conjecture from string theory.
We propose a new bound on the average null energy along a finite portion of a null geodesic. We believe our bound is valid on scales small compared to the radius of curvature in any quantum field theory that is consistently coupled to gravity. If correct, our bound implies that regions of negative energy density are never strongly gravitating, and that isolated regions of negative energy are forbidden.
I conjecture an upper bound on the number of possible swampland conjectures by comparing the entropy required by the conjectures themselves to the Beckenstein-Hawking entropy of the cosmological horizon. Assuming of order 100 kilobits of entropy per conjecture, this places an upper bound of order $10^{117}$ on the number of conjectures. I estimate the rate of production of swampland conjectures by the number of papers listed on INSPIRE with the word swampland in the title or abstract, which has been showing approximately exponential growth since 2014. At the current rate of growth, the entropy bound on the number of swampland conjectures can be projected to be saturated on a timescale of order $10^{-8} H_0^{-1}$. I compare the upper bound from the Swampland Conjecture Bound Conjecture (SCBC) to the estimated number of vacua in the string landscape. Employing the duality suggested by AdS/CFT between the quantum complexity of a holographic state and the volume of a Wheeler-Dewitt spacetime patch, I place a conservative lower bound of order $mathcal{N}_H > 10^{263}$ on the number of Hubble volumes in the multiverse which must be driven to heat death to fully explore the string landscape via conjectural methods.
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