Holographic inflation and holographic dark energy from entropy of the anti-de Sitter black hole

Abstract Based on the entropy of anti-de Sitter black hole, a new holographic dark energy model has been proposed. When the Hubble horizon and particle horizon are chosen as the IR cutoff, the late-time accelerated expansion of universe is realized. In this paper, we consider the Hubble horizon as the IR cutoff to investigate holographic inflation and slow-roll inflation in this model. We find that slow-roll inflation with the chaotic potential $$V_{0}\phi ^{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> is favored by Planck results for some special cases, such as $$n=1/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and $$n=1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , while holographic inflation is not supported by Planck results. Then, we analyze the reheating temperature and the number of reheating e-folds in this model, and we find that the results favor the cases $$n=1/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and $$n=1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Finally, we use the dynamical analysis method, statefinder diagnostic pairs, and the Hubble diagram to analyze this model. Our results indicate that when $$b^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> takes a small value, this model cannot be distinguished from the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model and can serve as an alternative to it.