Numerical Simulation of Axion Quintessence

Table 1

Parameters for the potential 𝑉=𝐴cos(𝜑). 𝑡₀ is the current age of the universe with 𝑡₀≡13.73 Gyr in the ΛCDM model, 0.1≤Ω_DE≤0.9 for 𝑡_0.1≤𝑡≤𝑡_0.9, the “coincidence” time interval Δ𝑡_𝑐=𝑡_0.9−𝑡_0.1, 𝑡_∗ is the turn-around time, 𝑡_𝑓 is the time of the big crunch, and 𝑎_∗=𝑎(𝑡_∗). All times are in Gyr. ∗For 𝜑_𝑖/𝜋 = 0.20 (0.23), Ω_DE≤ 0.85 (0.77) and in these cases 𝑡_0.9≡𝑡_0.85 and 𝑡_0.77, respectively.

𝜑𝑖/𝜋	𝐴/𝜌𝑐0	𝑤0	𝑡0	𝑡0.1	𝑡0.9	𝑡∗	𝑡𝑓	𝑡𝑐/𝑡𝑓	𝑎∗/𝑎0
0.05	0.73	−0.998	13.72	3.6	20.0	63.2	72.7	0.23	12.0
0.10	0.78	−0.99	13.70	3.5	20.3	47.6	56.8	0.30	5.0
0.15	0.88	−0.97	13.64	3.5	21.2	37.6	46.2	0.38	3.0
0.20	1.09	−0.93	13.49	3.3	21.2^*	29.2	37.0	0.48	2.0
0.23	1.41	−0.87	13.25	3.0	16.8^*	23.9	30.7	0.45	1.6