Towards a realistic solution of the cosmological constant fine-tuning problem by Higgs inflation

Why is the cosmological constant $\mathrm{\Lambda }$ observed today so much smaller than the Planck scale, and why is the Universe accelerating at present? This is the so-called cosmological constant fine-tuning problem. In this paper, we find that this problem may be solved with the help of Higgs inflation by simply assuming a variable cosmological “constant” during the inflationary epoch. Meanwhile, it could predict a large tensor-to-scalar ratio $r\approx 0.20$ and a large running of the spectral index $n_s^{\prime }\approx -0.028$ with a red-tilt spectrum $n_s\approx 0.96$, as well as a big enough number of $e$-folds $N\approx 40$, requiring that we solve the problems in big bang cosmology with the help of $\mathrm{\Lambda }$.

Figure 1

The present value of ${\mathrm{\Lambda }}_0$ (measured in units of $M_{\text{pl}}$.) vs the parameter $\alpha$. The dashed-orange, solid-black, and dotted-purple curves correspond to ${10}^5{\mathrm{\Omega }}_{\mathrm{\Lambda }}=1.3,1.4,1.5$, respectively. Here, the tensor-to-scalar ratio and the scalar power spectral index are fixed at $r=0.20$ and $n_s=0.96$, respectively.

Figure 2

The running of the scalar power spectral index $n_s^{\prime }$ vs the parameter $\alpha$. The dashed-orange, solid-black, and dotted-purple curves correspond to ${10}^5{\mathrm{\Omega }}_{\mathrm{\Lambda }}=1.3,1.4,1.5$, respectively. Here, the tensor-to-scalar ratio and the scalar power spectral index are fixed at $r=0.20$ and $n_s=0.96$, respectively.