de Sitter swampland conjecture in string field inflation
J. Sadeghi, Behnam Pourhassan, Saeed Noori Gashti, İzzet Sakallı, Mohammad Reza Alipour
Abstract
Abstract In this paper, we study a particular type of inflation by using non-local Friedman equations that are derived from the zero levels of string field theory and express a tachyonic action. Then, we challenge it by further refining de Sitter (dS) swampland conjecture (FRdSSC) monitoring. Therefore, we investigate some quantities, such as potential and Hubble parameters. We also consider slow-roll parameters to examine quantities such as the scalar spectrum index and the tensor-to-scalar ratio. Using straightforward calculations, we investigate this model from the swampland conjecture perspective in terms of the cosmological parameters, i.e., ( $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> ), ( r ), and observable data such as Planck 2018, by constructing some structures such as $$(c_{1,2}-n_s)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(c_{1,2}-r_s)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Then, we make a new restriction for this conjecture as $$c_1^2c_2^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> and get a limit for this model in the range $$c<0.0942$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.0942</mml:mn> </mml:mrow> </mml:math> . We find this inflationary model is strongly in tension with the dS swampland conjecture (dSSC), i.e., $$c_1=c_2 \ne {\mathcal {O}}(1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>≠</mml:mo> <mml:mi>O</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . So, we shall challenge it with the FRdSSC, which has some free parameters, viz., $$a,b>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , $$a+b=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , and $$q>2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . By setting these parameters, we examine the compatibility of the mentioned conjecture with this inflationary model. Finally, we infer from this string field inflation (SFI) model that it satisfies the FRdSSC with the constraint of its free parameters a , b , and q .