(Quasi-) de Sitter solutions across dimensions and the TCC bound
David Andriot, Ludwig Horer
Abstract
A bstract 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, $$ {M}_p\frac{\mid \nabla V\mid }{V}\ge c $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mfrac> <mml:mrow> <mml:mo>∣</mml:mo> <mml:mo>∇</mml:mo> <mml:mi>V</mml:mi> <mml:mo>∣</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> </mml:mfrac> <mml:mo>≥</mml:mo> <mml:mi>c</mml:mi> </mml:math> . Remarkably, the TCC bound $$ c\ge \frac{2}{\sqrt{\left(d-1\right)\left(d-2\right)}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>c</mml:mi> <mml:mo>≥</mml:mo> <mml:mfrac> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:msqrt> </mml:mfrac> </mml:math> 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.