In search of global 21-cm signal using artificial neural network in light of ARCADE 2

Abstract Understanding the astrophysical nature of the first stars remains an unsolved problem in cosmology. The redshifted global 21-cm signal $$({T}_{21})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>21</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> acts as a treasure trove to probe the cosmic dawn era – when the intergalactic medium was mostly neutral. Many experiments, like SARAS 3, EDGES, and DARE, have been proposed to probe the cosmic dawn era. However, extracting the faint cosmological signal buried inside a brighter foreground, $${\mathcal {O}}(10^4)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , remains challenging. Additionally, an accurate modelling of foreground and $${T}_{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>21</mml:mn> </mml:msub> </mml:math> signal remains the heart of any extraction technique. In this work, we constructed the foreground signal $$(T_{FG})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>FG</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> from the global sky model and star formation history using Press–Schechter formalism to determine the $$T_{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>21</mml:mn> </mml:msub> </mml:math> signal with excess radio background following ARCADE 2 detection. Further, we incorporated static ionospheric distortion into the total signal and calculated the signal measured by an ideal antenna. We then trained an artificial neural network (ANN) for the extraction of a $$T_{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>21</mml:mn> </mml:msub> </mml:math> signal parameters signal measured by antenna with an R-square score $$(0.5523{-}0.9901)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0.5523</mml:mn> <mml:mo>-</mml:mo> <mml:mn>0.9901</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Lastly, we used a Bayesian technique to extract $$T_{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>21</mml:mn> </mml:msub> </mml:math> signal and compared the finding with ANN’s extraction.