We consider attractor behaviour of holographic inflation model based on a dynamic of the D3-brane located at the holographic boundary of an asymptotic AdS5 bulk [1,2]. Using dynamical equation of the Hamilton-Jacobi type we show that the solutions for the tachyon field have properties of the attractor in the cosmological context [3]. The numerical solutions of the dynamical equation in the phase-space are examined for the case of inverse cosine hyperbolic potential and exponential tachyon potential [4]. We use attractor properties to fix initial values of tachyon field and to calculate the most important observational parameters for inflation [5].
References
[1] D.D. Dimitrijevic, N. Bilić, G.S. Djordjevic, M. Milosevic, M. Stojanovic, Tachyon scalar field in a braneworld cosmology, Int. J. Mod. Phys. A (2018), Vol 33, No. 34.
[2] N. Bilić, D.D. Dimitrijević, G.S. Djordjevic, M. Milošević, M. Stojanović, Tachyon inflation in the holographic braneworld, J. Cosmol. Astropart. Phys. (2019) 034–034.
[3] M. Stojanović, M. Milošević, G.S. Djordjević and D.D. Dimitrijević, Holographic Inflation with Tachyon Field as an Attractor Solution, SFIN year XXXIII Series A: Conferences (2020), No. A1, 311-318.
[4] D.D. Dimitrijević, G. Djordjević, M. Milošević and M. Stojanović, Attractor Behaviour of Holographic Inflation Model for Inverse Cosine Hyperbolic Potential, Facta Universitatis, Series: Physics, Chemistry and Technology (2020), Vol. 18, No 1, 65-73.
[5] M. Milošević, D.D. Dimitrijević, G.S. Djordjević and M.D. Stojanović, Dynamics of Tachyon Fields and Inflation – Comparison of Analytical and Numerical Results with Observation, Serbian Astronomical Journal (2016), Vol. 192, 1-8.