(Quasi-) de Sitter solutions across dimensions and the TCC bound

Abstract

In this work, we investigate the existence of string theory solutions with a d-dimensional (quasi-) de Sitter spacetime, for 3 ≤ d ≤ 10. Considering classical compactifications, we derive no-go theorems valid for general d. We use them to exclude (quasi-) de Sitter solutions for d ≥ 7. In addition, such solutions are found unlikely to exist in d = 6, 5. For each no-go theorem, we further compute the d-dependent parameter c of the swampland de Sitter conjecture, $$ {M}_p\frac{\mid \nabla V\mid }{V}\ge c $$ M p ∣ ∇ V ∣ V ≥ c . Remarkably, the TCC bound $$ c\ge \frac{2}{\sqrt{\left(d-1\right)\left(d-2\right)}} $$ c ≥ 2 d − 1 d − 2 is then perfectly satisfied for d ≥ 4, with several saturation cases. However, we observe a violation of this bound in d = 3. We finally comment on related proposals in the literature, on the swampland distance conjecture and its decay rate, and on the so-called accelerated expansion bound.

Accelerating universe at the end of time

“…Another result of our analysis is that the slow-roll approximation can also be ruled out by our no-go result. This conclusion is in line with previous findings in the string-theory literature [18][19][20][21][22][23][24] though we hasten to add that such claims are based on the gradient and curvature of the potential, which, as we have shown, are not the right criteria for cosmic acceleration in general. On the other hand, transient solutions -viable for inflation -are not within the reach of the current analysis.…”

Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture

“…of the ATCC bounds in d ≥ 4, providing a confirmation of the above. We find several violations in d = 3, as already noticed for the TCC in [34]: this can be understood from the peculiarity of gravity in d = 3.…”

“…The ATCC also brings a physics argument behind those results, related to the regime of validity of a quantum gravity effective theory, thanks to our refinement of the TCC. This argument may explain why the checks of the TCC [34,39] have so far been so successful. Last but not least, we found the new condition (1.8) on the second derivative, whose surprising consequences have just been mentioned.…”

Bumping into the Species Scale with the Scalar Potential

“…If () is an effective theory of quantum gravity, its typical energy scales, below its cut‐off, should be smaller than the quantum gravity scale. A typical energy scale of () is that of the scalar potential, corresponding to $$\sqrt {V}/M_p$$, so one may bound it by a Planckian scale (see the refined TCC, and the ATCC, for a use of this argument [ 23 ] ). Given the above, one may be more constraining and bound it by the species scale, giving $$$$\begin{equation} \Lambda _s \ge \frac{\sqrt {V}}{M_p} \ .$$…”

“…V∕M p , so one may bound it by a Planckian scale (see the refined TCC, and the ATCC, for a use of this argument [23] ). Given the above, one may be more constraining and bound it by the species scale, giving…”