Late time transition in the evolution of the Universe

The late time crossover from a power-law to an exponential expansion of the Universe evolution is the major problem in today’s physical cosmology. Unless this critical transition problem is solved, it is not possible to reach a holistic theory of cosmology. In this study, we propose a simple model in the FLRW framework, where dark matter and dark energy interact through a potential. We analytically solve this model and obtain scale factor a(t) from the presented model. Mainly, employing numerical solutions we show that the scale parameter has a hybrid form which includes power and exponential terms. The numerical results clearly show that there is a time crossover tc in the scale factor a(t) curve, which indicates the transition from the power-law to the exponential expansion of the Universe. We fit these unscaled curves and obtain that scale factor behaves as a(t) ∝ t 2/3 below t ≤ tc, and as a(t) ∝ exp(H0t) with H0 = 0.4 and H0 = 0.3 for the relatively weak and strong interactions above t > tc, respectively. It is the first time that we explicitly obtain a hybrid scale factor incorporating the power and exponential terms as a(t) ∝ t 2/3 e H0t . We conclude that the presented model can solve the late time transition problem of the Universe based on dark matter and dark energy interaction. Additionally, we numerically obtain other kinematic parameters depending upon the scale factor. We discuss the limit behaviors of all relevant cosmological parameters. Our results are completely in good agreement with observational data. Finally, we state that this work makes essential steps towards solving a critical outstanding problem of the cosmology, and has a potential to creates a paradigm for future studies in this field.

Late time transition in the evolution of the Universe

The late time crossover from a power-law to an exponential expansion of the Universe evolution is the major problem in today’s physical cosmology. Unless this critical transition problem is solved, it is not possible to reach a holistic theory of cosmology. In this study, we propose a simple model in the FLRW framework, where dark matter and dark energy interact through a potential. We analytically solve this model and obtain scale factor a(t) from the presented model. Mainly, employing numerical solutions we show that the scale parameter has a hybrid form which includes power and exponential terms. The numerical results clearly show that there is a time crossover tc in the scale factor a(t) curve, which indicates the transition from the power-law to the exponential expansion of the Universe. We fit these unscaled curves and obtain that scale factor behaves as a(t) ∝ t2/3 below t ≤ tc, and as a(t) ∝ exp(H0t) with H0 = 0.4 and H0 = 0.3 for the relatively weak and strong interactions above t > tc, respectively. It is the first time that we explicitly obtain a hybrid scale factor incorporating the power and exponential terms as a(t) ∝ t2/3eH0t . We conclude that the presented model can solve the late time transition problem of the Universe based on dark matter and dark energy interaction. Additionally, we numerically obtain other kinematic parameters depending upon the scale factor. We discuss the limit behaviors of all relevant cosmological parameters. Our results are completely in good agreement with observational data. Finally, we state that this work makes essential steps towards solving a critical outstanding problem of the cosmology, and has a potential to creates a paradigm for future studies in this field.

A BeiDou Signal Acquisition Approach Using Variable Length Data Accumulation Based on Signal Delay and Multiplication

The secondary modulation with the Neumann-Hoffman code increases the possibility of bit sign transition. Unlike other GNSS signals, there is no pilot component for synchronization in BeiDou B1/B3 signals, which increases the complexity in acquisition. A previous study has shown that the delay and multiplication (DAM) method is able to eliminate the bit sign transition problem, but it only applies to pretty strong signals. In this paper, a DAM-based BeiDou signal acquisition approach, called variable length data accumulation (VLDA), is proposed to acquire weak satellite signals. Firstly, the performance of DAM method versus the different delays is analyzed. The DAM operation not only eliminates bit sign transition, but it also increases noise power. Secondly, long-term signal is periodically accumulated to improve signal intensity in order to acquire weak signals. While considering the Doppler frequency shift of ranging codes, the signal length must be compensated before accumulating long-term signal. Finally, the fast-Fourier-transform based parallel code phase algorithm are used for acquisition. The simulation results indicate that the proposed VLDA method has better acquisition sensitivity than traditional non-coherent integration method under the same calculation amount. The VLDA method only requires approximately 27.5% of calculations to achieve the same acquisition sensitivity (35 dBHz). What is more, the actual experimental results verify the feasibility of the VLDA method. It can be concluded that the proposed approach is an effective and feasible method for solving the bit sign transition problem.